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Ang, Eu-Jin. "Brownian motion queueing models of communications and manufacturing systems." Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298242.
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Karangwa, Innocent. "Comparing South African financial markets behaviour to the geometric Brownian Motion Process." Thesis, University of the Western Cape, 2008. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_4787_1363778247.
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This study examines the behaviour of the South African financial markets with regards to the Geometric Brownian motion process. It uses the daily, weekly, and monthly stock returns time series of some major securities trading in the South African financial market, more specifically the US dollar/Euro, JSE ALSI Total Returns Index, South African All Bond Index, Anglo American Corporation, Standard Bank, Sasol, US dollar Gold Price , Brent spot oil price, and South African white maize near future. The assumptions underlying the
Geometric Brownian motion in finance, namely the stationarity, the normality and the independence of stock returns, are tested using both graphical (histograms and normal plots)
and statistical test (Kolmogorov-Simirnov test, Box-Ljung statistic and Augmented Dickey-Fuller test) methods to check whether or not the Brownian motion as a model for South
African financial markets holds. The Hurst exponent or independence index is also applied to support the results from the previous test. Theoretically, the independent or Geometric
Brownian motion time series should be characterised by the Hurst exponent of ½
. A value of a Hurst exponent different from that would indicate the presence of long memory or
fractional Brownian motion in a time series. The study shows that at least one assumption is violated when the Geometric Brownian motion process is examined assumption by
assumption. It also reveals the presence of both long memory and random walk or Geometric Brownian motion in the South African financial markets returns when the Hurst index analysis is used and finds that the Currency market is the most efficient of the South African financial markets. The study concludes that although some assumptions underlying the
rocess are violated, the Brownian motion as a model in South African financial markets can not be rejected. It can be accepted in some instances if some parameters such as the Hurst exponent are added.
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Cai, Chunhao. "Analyse statistique de quelques modèles de processus de type fractionnaire." Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1030/document.
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Cette thèse porte sur l’analyse statistique de quelques modèles de processus stochastiques gouvernés par des bruits de type fractionnaire, en temps discret ou continu.Dans le Chapitre 1, nous étudions le problème d’estimation par maximum de vraisemblance (EMV) des paramètres d’un processus autorégressif d’ordre p (AR(p)) dirigé par un bruit gaussien stationnaire, qui peut être à longue mémoire commele bruit gaussien fractionnaire. Nous donnons une formule explicite pour l’EMV et nous analysons ses propriétés asymptotiques. En fait, dans notre modèle la fonction de covariance du bruit est supposée connue, mais le comportement asymptotique de l’estimateur (vitesse de convergence, information de Fisher) n’en dépend pas.Le Chapitre 2 est consacré à la détermination de l’entrée optimale (d’un point de vue asymptotique) pour l’estimation du paramètre de dérive dans un processus d’Ornstein-Uhlenbeck fractionnaire partiellement observé mais contrôlé. Nous exposons un principe de séparation qui nous permet d’atteindre cet objectif. Les propriétés asymptotiques de l’EMV sont démontrées en utilisant le programme d’Ibragimov-Khasminskii et le calcul de transformées de Laplace d’une fonctionnellequadratique du processus.Dans le Chapitre 3, nous présentons une nouvelle approche pour étudier les propriétés du mouvement brownien fractionnaire mélangé et de modèles connexes, basée sur la théorie du filtrage des processus gaussiens. Les résultats mettent en lumière la structure de semimartingale et mènent à un certain nombre de propriétés d’absolue continuité utiles. Nous établissons l’équivalence des mesures induites par le mouvement brownien fractionnaire mélangé avec une dérive stochastique, et en déduisons l’expression correspondante de la dérivée de Radon-Nikodym. Pour un indice de Hurst H > 3=4, nous obtenons une représentation du mouvement brownien fractionnaire mélangé comme processus de type diffusion dans sa filtration naturelle et en déduisons une formule de la dérivée de Radon-Nikodym par rapport à la mesurede Wiener. Pour H < 1=4, nous montrons l’équivalence de la mesure avec celle la composante fractionnaire et obtenons une formule pour la densité correspondante. Un domaine d’application potentielle est l’analyse statistique des modèles gouvernés par des bruits fractionnaires mélangés. A titre d’exemple, nous considérons le modèle de régression linéaire de base et montrons comment définir l’EMV et étudié son comportement asymptotiqueThis thesis focuses on the statistical analysis of some models of stochastic processes generated by fractional noise in discrete or continuous time.In Chapter 1, we study the problem of parameter estimation by maximum likelihood (MLE) for an autoregressive process of order p (AR (p)) generated by a stationary Gaussian noise, which can have long memory as the fractional Gaussiannoise. We exhibit an explicit formula for the MLE and we analyze its asymptotic properties. Actually in our model the covariance function of the noise is assumed to be known but the asymptotic behavior of the estimator ( rate of convergence, Fisher information) does not depend on it.Chapter 2 is devoted to the determination of the asymptotical optimal input for the estimation of the drift parameter in a partially observed but controlled fractional Ornstein-Uhlenbeck process. We expose a separation principle that allows us toreach this goal. Large sample asymptotical properties of the MLE are deduced using the Ibragimov-Khasminskii program and Laplace transform computations for quadratic functionals of the process.In Chapter 3, we present a new approach to study the properties of mixed fractional Brownian motion (fBm) and related models, based on the filtering theory of Gaussian processes. The results shed light on the semimartingale structure andproperties lead to a number of useful absolute continuity relations. We establish equivalence of the measures, induced by the mixed fBm with stochastic drifts, and derive the corresponding expression for the Radon-Nikodym derivative. For theHurst index H > 3=4 we obtain a representation of the mixed fBm as a diffusion type process in its own filtration and derive a formula for the Radon-Nikodym derivative with respect to the Wiener measure. For H < 1=4, we prove equivalenceto the fractional component and obtain a formula for the corresponding derivative. An area of potential applications is statistical analysis of models, driven by mixed fractional noises. As an example we consider only the basic linear regression setting and show how the MLE can be defined and studied in the large sample asymptotic regime
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Lebovits, Joachim. "Stochastic calculus with respect to multi-fractional Brownian motion and applications to finance." Phd thesis, Châtenay-Malabry, Ecole centrale de Paris, 2012. http://tel.archives-ouvertes.fr/tel-00704526.
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The aim of this PhD Thesis was to build and develop a stochastic calculus (in particular a stochastic integral) with respect to multifractional Brownian motion (mBm). Since the choice of the theory and the tools to use was not fixed a priori, we chose the White Noise theory which generalizes, in the case of fractional Brownian motion (fBm) , the Malliavin calculus. The first chapter of this thesis presents several notions we will use in the sequel.In the second chapter we present a construction as well as the main properties of stochastic integral with respect to harmonizable mBm.We also give Ito formulas and a Tanaka formula with respect to this mBm. In the third chapter we give a new definition, simplier and generalier of multifractional Brownian motion. We then show that mBm appears naturally as a limit of a sequence of fractional Brownian motions of different Hurst index.We then use this idea to build an integral with respect to mBm as a limit of sum of integrals with respect ot fBm. This being done we particularize this definition to the case of Malliavin calculus and White Noise theory. In this last case we compare the integral hence defined to the one we got in chapter 2. The fourth and last chapter propose a multifractional stochastic volatility model where the process of volatility is driven by a mBm. The interest lies in the fact that we can hence take into account, in the same time, the long range dependence of increments of volatility process and the fact that regularity vary along the time.Using the functional quantization theory in order to, among other things, approximate the solution of stochastic differential equations, we can compute the price of forward start options and then get and plot the implied volatility nappe that we graphically represent.
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Graf, Ferdinand. "Exotic Option Pricing in Stochastic Volatility Levy Models and with Fractional Brownian Motion." [S.l. : s.n.], 2007. http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-35340.
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Bauke, Francisco Conti. "Portadores quentes : modelo browniano /." Rio Claro : [s.n.], 2011. http://hdl.handle.net/11449/91881.
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Orientador: Roberto E. Lagos MonacoBanca: José Antonio Roversi
Banca: Bernardo Laks
Resumo: Neste trabalho estudamos o modelo do movimento Browniano de uma partícula carregada sob a ação de campos elétrico e magnético, externos e homogêneos, no formalismo de Langevin. Calculamos a energia cinética média através do teorema da flutuação-dissipação e obtivemos uma expressão para a temperatura efetiva das partículas Brownianas em função da temperatura do reservatório e dos campos externos. Esta temperatura efetiva mostrou-se sempre maior que a temperatura do reservatório, o que explica a expressão "portadores quentes". Estudamos essa temperatura efetiva no regime assintótico, ou seja, no estado estacionário atingido em tempos muito longos (quando comparado com o tempo de colisão) e a utilizamos para escrever as equações de transporte em semicondutores, denominadas equações de Shockley generalizadas sendo que incluem nesse caso também a ação do campo magnético. Uma aplicação direta e relevante foi a modelagem para o já conhecido efeito Gunn para portadores assumidos como Brownianos. A temperatura efetiva calculada por nós no regime transiente permitiu estudar também os efeitos do reservatório na relaxação da temperatura efetiva à temperatura terminal (de não equilíbrio e estacionária). Nossos resultados no que diz respeito ao efeito Gunn, embora seja o modelo mais simples de um portador Browniano, mostrou uma surpreendente concordância com resultados experimentais, sugerindo que modelos mais sofisticados devam incluir os elementos apresentados neste estudo
Abstract: We present a Brownian model for a charged particle in a field of forces, in particular, electric and magnetic external homogeneous fields, within the Langevin formalism. We compute the average kinetic energy via the fluctuation dissipation and obtain an expression for the Brownian particle's effective temperature. The latter is a function of the heat bath temperature and both external fields. This effective temperature is always greater than the heat bath temperature, therefore the expression "hot carriers". This effective temperature, in the asymptotic regime, the stationary state at long times (greater than the collision time), is used to write down the transport equations for semiconductors, namely the generalized Shockley equations, now incorporating the magnetic field effect. A direct and relevant application follows: a model for the well known Gunn effect, assuming a Brownian scheme. In the transient regime the computed effective temperature also allow us to probe some features of the heat bath, as the effective temperature relaxes to its terminal stationary value. As for our results in the Gunn effect model, the simplest of all in a Brownian scheme, we obtain a surprisingly good agreement with experimental data, suggesting that more involved models should include our minimal assumptions
Mestre
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Bauke, Francisco Conti [UNESP]. "Portadores quentes: modelo browniano." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/91881.
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Neste trabalho estudamos o modelo do movimento Browniano de uma partícula carregada sob a ação de campos elétrico e magnético, externos e homogêneos, no formalismo de Langevin. Calculamos a energia cinética média através do teorema da flutuação-dissipação e obtivemos uma expressão para a temperatura efetiva das partículas Brownianas em função da temperatura do reservatório e dos campos externos. Esta temperatura efetiva mostrou-se sempre maior que a temperatura do reservatório, o que explica a expressão “portadores quentes”. Estudamos essa temperatura efetiva no regime assintótico, ou seja, no estado estacionário atingido em tempos muito longos (quando comparado com o tempo de colisão) e a utilizamos para escrever as equações de transporte em semicondutores, denominadas equações de Shockley generalizadas sendo que incluem nesse caso também a ação do campo magnético. Uma aplicação direta e relevante foi a modelagem para o já conhecido efeito Gunn para portadores assumidos como Brownianos. A temperatura efetiva calculada por nós no regime transiente permitiu estudar também os efeitos do reservatório na relaxação da temperatura efetiva à temperatura terminal (de não equilíbrio e estacionária). Nossos resultados no que diz respeito ao efeito Gunn, embora seja o modelo mais simples de um portador Browniano, mostrou uma surpreendente concordância com resultados experimentais, sugerindo que modelos mais sofisticados devam incluir os elementos apresentados neste estudo
We present a Brownian model for a charged particle in a field of forces, in particular, electric and magnetic external homogeneous fields, within the Langevin formalism. We compute the average kinetic energy via the fluctuation dissipation and obtain an expression for the Brownian particle´s effective temperature. The latter is a function of the heat bath temperature and both external fields. This effective temperature is always greater than the heat bath temperature, therefore the expression “hot carriers”. This effective temperature, in the asymptotic regime, the stationary state at long times (greater than the collision time), is used to write down the transport equations for semiconductors, namely the generalized Shockley equations, now incorporating the magnetic field effect. A direct and relevant application follows: a model for the well known Gunn effect, assuming a Brownian scheme. In the transient regime the computed effective temperature also allow us to probe some features of the heat bath, as the effective temperature relaxes to its terminal stationary value. As for our results in the Gunn effect model, the simplest of all in a Brownian scheme, we obtain a surprisingly good agreement with experimental data, suggesting that more involved models should include our minimal assumptions
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Mvondo, Bernardin Gael. "Numerical techniques for optimal investment consumption models." University of the Western Cape, 2014. http://hdl.handle.net/11394/4352.
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>Magister Scientiae - MScThe problem of optimal investment has been extensively studied by numerous researchers in order to generalize the original framework. Those generalizations have been made in different directions and using different techniques. For example, Perera [Optimal consumption, investment and insurance with insurable risk for an investor in a Levy market, Insurance: Mathematics and Economics, 46 (3) (2010) 479-484] applied the martingale approach to obtain a closed form solution for the optimal investment, consumption and insurance strategies of an individual in the presence of an insurable risk when the insurable risk and risky asset returns are described by Levy processes and the utility is a constant absolute risk aversion. In another work, Sattinger [The Markov consumption problem, Journal of Mathematical Economics, 47 (4-5) (2011) 409-416] gave a model of consumption behavior under uncertainty as the solution to a continuous-time dynamic control problem in which an individual moves between employment and unemployment according to a Markov process. In this thesis, we will review the consumption models in the above framework and will simulate some of them using an infinite series expansion method − a key focus of this research. Several numerical results obtained by using MATLAB are presented with detailed explanations.
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Teichmann, Jakob. "Stochastic modeling of Brownian and turbulent coagulation." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2017. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-220625.
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Als Beitrag zu einer verbesserten Filtration von Metallschmelzen werden stochastische Modelle für den essentiellen Mechanismus der Koagulation von Brownschen Partikeln und Partikeln in turbulenten Strömungen entwickelt und untersucht. Formeln für die zeitliche Entwicklung der Partikelkonzentration in diesen Systemen erlauben die Bestimmung von physikalischen Parametern, welche die Koagulation und somit die Filtration begünstigen. Um wichtige Resultate im Zusammenhang mit der traditionellen Herangehensweise für Brownsche Partikel zu berichtigen und zu erweitern, wird ein neuer Ansatz in Form zweier Modelle entwickelt. Für beide werden Formeln für die Partikelkonzentration, auf Basis einer neuartigen Verallgemeinerung der Matérn Hard-Core-Punktprozesse, abgeleitet. Um im Hinblick auf die Koagulationsgleichung der fraktalartigen Gestalt der Agglomerate besser Rechnung zu tragen, wird deren Morphologie anhand zweier neuer Modelle quantifiziert. Die Arbeit wird durch Anwendung der Modelle und numerische Simulationen von Koagulation und Abscheidung in turbulenten Strömungen abgerundet.
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Nouri, Suhila Lynn. "Expected maximum drawdowns under constant and stochastic volatility." Link to electronic thesis, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-050406-151319/.
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Mohaupt, Mikaël. "Modélisation et simulation de l'agglomération des colloïdes dans un écoulement turbulent." Thesis, Vandoeuvre-les-Nancy, INPL, 2011. http://www.theses.fr/2011INPL068N/document.
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Ce travail de thèse porte sur la modélisation et la simulation numérique de la collision et l'agglomération de particules colloïdales dans un écoulement fluide turbulent par une nouvelle méthode. Ces particules sont sensibles dans une même mesure aux effets brownien et turbulent. La première partie du travail concerne la modélisation du phénomène physique,allant du transport des particules jusqu'à la modélisation des forces d'adhésion physico-chimiques en passant par l'étape cruciale qui est la détection des interactions entre les particules (collisions). Cette détection des collisions est dans un premier temps étudiée par rapport aux algorithmes classiques existants dans la littérature. Bien que très efficaces dans le cadre de particules soumises à l'agitation turbulente, les conclusions de cette partie exposent les limites des méthodes existantes en termes de coûts numériques, pour le traitement d'un ensemble de colloïdes soumis au mouvement brownien. La seconde partie du travail oriente alors les travaux vers une vision novatrice du phénomène physique considéré. Le caractère diffusif aléatoire est alors considéré d'un point de vu stochastique, comme un processus conditionné dans l'espace et dans le temps. Ainsi, une nouvelle méthode de détection et de traitement des collisions de particules soumises exclusivement à un mouvement diffusif est présentée et validée, exposant un gain considérable en termes de coûts numériques. Le potentiel de cette nouvelle approche est validé et ouvre de nombreuses pistes de réflexion dans l'utilisation des méthodes stochastiques appliqués à la représentation de la physiquePh.D thesis focuses on modeling and numerical simulation of collision and agglomeration of colloidal particles in a turbulent flow by using a new method. These particles are affected by both Brownian and turbulent effects. The first part of the work deals with current models of the physical phenomenon, from the transport of single particles to a model for physico-chemical adhesive forces, and points out the critical step which is the detection of interactions between particles (collisions). This detection is initially studied by applying classical algorithms existing in the literature. Although they are very efficient in the context of particles subject to turbulent agitation, first conclusions show the limitations of these existing methods in terms of numerical costs, considering the treatment of colloids subject to the Brownian motion. The second part of this work proposes a new vision of the physical phenomenon focusing on the random diffusive behaviour. This issue is adressed from a stochastic point of view as a process conditionned in space and time. Thus, a new method for the detection and treatment of collisions is presented and validated, which represents considerable gain in terms of numerical cost. The potential of this new approach is validated and opens new opportunities for the use of stochastic methods applied to the representation of physics
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Chen, Yaming. "Dynamical properties of piecewise-smooth stochastic models." Thesis, Queen Mary, University of London, 2014. http://qmro.qmul.ac.uk/xmlui/handle/123456789/9129.
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Piecewise-smooth stochastic systems are widely used in engineering science. However, the theory of these systems is only in its infancy. In this thesis, we take as an example the Brownian motion with dry friction to illustrate dynamical properties of these systems with respect to three interesting topics: (i) weak-noise approximations, (ii) first-passage time (FPT) problems and (iii) functionals of stochastic processes. Firstly, we investigate the validity and accuracy of weak-noise approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example the Brownian motion with pure dry friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided that the singularity of the path integral is treated with some heuristics. We also consider a smooth regularisation of this piecewise-constant SDE and study to what extent this regularisation can rectify some of the problems encountered in the non-smooth case. Secondly, we provide analytic solutions to the FPT problem of the Brownian motion with dry friction. For the pure dry friction case, we find a phase transition phenomenon in the spectrum which relates to the position of the exit point and affects the tail of the FPT distribution. For the model with dry and viscous friction, we evaluate quantitatively the impact of the corresponding stick-slip transition and of the transition to ballistic exit. We also derive analytically the distributions of the maximum velocity till the FPT for the dry friction model. Thirdly, we generalise the so-called backward Fokker-Planck technique and obtain a recursive ordinary differential equation for the moments of functionals in the Laplace space. We then apply the developed results to analyse the local time, the occupation time and the displacement of the dry friction model. Finally, we conclude this thesis and state some related unsolved problems.
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Londani, Mukhethwa. "Numerical Methods for Mathematical Models on Warrant Pricing." University of the Western Cape, 2010. http://hdl.handle.net/11394/8210.
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>Magister Scientiae - MScWarrant pricing has become very crucial in the present market scenario. See, for example, M. Hanke and K. Potzelberger, Consistent pricing of warrants and traded options, Review Financial Economics 11(1) (2002) 63-77 where the authors indicate that warrants issuance affects the stock price process of the issuing company. This change in the stock price process leads to subsequent changes in the prices of options written on the issuing company's stocks. Another notable work is W.G. Zhang, W.L. Xiao and C.X. He, Equity warrant pricing model under Fractional Brownian motion and an empirical study, Expert System with Applications 36(2) (2009) 3056-3065 where the authors construct equity warrants pricing model under Fractional Brownian motion and deduce the European options pricing formula with a simple method. We study this paper in details in this mini-thesis. We also study some of the mathematical models on warrant pricing using the Black-Scholes framework. The relationship between the price of the warrants and the price of the call accounts for the dilution effect is also studied mathematically. Finally we do some numerical simulations to derive the value of warrants.
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Mawoussi, Kodjo. "Effet de l'encombrement des protéines sur la diffusion des lipides et des protéines membranaires." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066541/document.
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La diffusion latérale des lipides et des protéines transmembranaires est essentielle pour les fonctions biologiques. Dans le contexte cellulaire, la fraction surfacique des protéines membranaires est élevée, atteignant environ de 50 à 70% selon le type de membrane. La diffusion se fait donc dans un milieu très encombré. Le but de ce travail est d'étudier in vitro l'effet de l'encombrement des protéines sur la diffusion des protéines et des lipides. Jusqu'à présent, les mesures de diffusion latérale ont généralement été réalisées à faible densité de protéines, et l'effet de l'encombrement des inclusions membranaires ou des protéines membranaires a été peu étudié expérimentalement. Nous avons utilisé une méthode de suivi de particules uniques (SPT) pour suivre les trajectoires de la pompe à protons Bactériorhodopsine (BR) et de lipides marqués avec des quantum dots au bas de vésicules unilamellaires géantes (GUVs) en fonction de la fraction de surface totale (Ф) de BR reconstituée dans la membrane constituée par ailleurs de 1,2-Dioleoyl-sn-glycéro-3-phosphocholine (DOPC)Lateral diffusion of lipids and transmembrane proteins is essential for biological functions. In the cellular context, the surface fraction of membrane proteins is high, reaching approximately 50 to 70% depending on the membrane type. Therefore, diffusion occurs in a very crowded environment. The aim of this work is to study in vitro the effect of protein crowding on their own diffusion and on those of the surrounding lipids. So far, lateral diffusion measurements generally have been carried out at low protein density, and the effect of proteins crowding has not been much studied experimentally. We used a single particle tracking (SPT) method to track the trajectories of the Bacterorhodopsin (BR) proton pump and of lipids labeled with quantum dots at the bottom of giant unilamellar vesicles (GUVs) as a function of the total surface fraction (Ф) of BR reconstituted in 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) membrane
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Walljee, Raabia. "The Levy-LIBOR model with default risk." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96957.
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Thesis (MSc)--Stellenbosch University, 2015ENGLISH ABSTRACT : In recent years, the use of Lévy processes as a modelling tool has come to be viewed more favourably than the use of the classical Brownian motion setup. The reason for this is that these processes provide more flexibility and also capture more of the ’real world’ dynamics of the model. Hence the use of Lévy processes for financial modelling is a motivating factor behind this research presentation. As a starting point a framework for the LIBOR market model with dynamics driven by a Lévy process instead of the classical Brownian motion setup is presented. When modelling LIBOR rates the use of a more realistic driving process is important since these rates are the most realistic interest rates used in the market of financial trading on a daily basis. Since the financial crisis there has been an increasing demand and need for efficient modelling and management of risk within the market. This has further led to the motivation of the use of Lévy based models for the modelling of credit risky financial instruments. The motivation stems from the basic properties of stationary and independent increments of Lévy processes. With these properties, the model is able to better account for any unexpected behaviour within the market, usually referred to as "jumps". Taking both of these factors into account, there is much motivation for the construction of a model driven by Lévy processes which is able to model credit risk and credit risky instruments. The model for LIBOR rates driven by these processes was first introduced by Eberlein and Özkan (2005) and is known as the Lévy-LIBOR model. In order to account for the credit risk in the market, the Lévy-LIBOR model with default risk was constructed. This was initially done by Kluge (2005) and then formally introduced in the paper by Eberlein et al. (2006). This thesis aims to present the theoretical construction of the model as done in the above mentioned references. The construction includes the consideration of recovery rates associated to the default event as well as a pricing formula for some popular credit derivatives.
AFRIKAANSE OPSOMMING : In onlangse jare, is die gebruik van Lévy-prosesse as ’n modellerings instrument baie meer gunstig gevind as die gebruik van die klassieke Brownse bewegingsproses opstel. Die rede hiervoor is dat hierdie prosesse meer buigsaamheid verskaf en die dinamiek van die model wat die praktyk beskryf, beter hierin vervat word. Dus is die gebruik van Lévy-prosesse vir finansiële modellering ’n motiverende faktor vir hierdie navorsingsaanbieding. As beginput word ’n raamwerk vir die LIBOR mark model met dinamika, gedryf deur ’n Lévy-proses in plaas van die klassieke Brownse bewegings opstel, aangebied. Wanneer LIBOR-koerse gemodelleer word is die gebruik van ’n meer realistiese proses belangriker aangesien hierdie koerse die mees realistiese koerse is wat in die finansiële mark op ’n daaglikse basis gebruik word. Sedert die finansiële krisis was daar ’n toenemende aanvraag en behoefte aan doeltreffende modellering en die bestaan van risiko binne die mark. Dit het verder gelei tot die motivering van Lévy-gebaseerde modelle vir die modellering van finansiële instrumente wat in die besonder aan kridietrisiko onderhewig is. Die motivering spruit uit die basiese eienskappe van stasionêre en onafhanklike inkremente van Lévy-prosesse. Met hierdie eienskappe is die model in staat om enige onverwagte gedrag (bekend as spronge) vas te vang. Deur hierdie faktore in ag te neem, is daar genoeg motivering vir die bou van ’n model gedryf deur Lévy-prosesse wat in staat is om kredietrisiko en instrumente onderhewig hieraan te modelleer. Die model vir LIBOR-koerse gedryf deur hierdie prosesse was oorspronklik bekendgestel deur Eberlein and Özkan (2005) en staan beken as die Lévy-LIBOR model. Om die kredietrisiko in die mark te akkommodeer word die Lévy-LIBOR model met "default risk" gekonstrueer. Dit was aanvanklik deur Kluge (2005) gedoen en formeel in die artikel bekendgestel deur Eberlein et al. (2006). Die doel van hierdie tesis is om die teoretiese konstruksie van die model aan te bied soos gedoen in die bogenoemde verwysings. Die konstruksie sluit ondermeer in die terugkrygingskoers wat met die wanbetaling geassosieer word, sowel as ’n prysingsformule vir ’n paar bekende krediet afgeleide instrumente.
16
Arikan, Ali Ferda. "Structural models for the pricing of corporate securities and financial synergies : applications with stochastic processes including arithmetic Brownian motion." Thesis, University of Bradford, 2010. http://hdl.handle.net/10454/5416.
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Mergers are the combining of two or more firms to create synergies. These synergies may come from various sources such as operational synergies come from economies of scale or financial synergies come from increased value of securities of the firm. There are vast amount of studies analysing operational synergies of mergers. This study analyses the financial ones. This way the dynamics of purely financial synergies can be revealed. Purely financial synergies can be transformed into financial instruments such as securitization. While analysing financial synergies the puzzle of distribution of financial synergies between claimholders is investigated. Previous literature on mergers showed that bondholders may gain more than existing shareholders of the merging firms. This may become rather controversial. A merger may be synergistic but it does not necessarily mean that shareholders' wealth will increase. Managers and/or shareholders are the parties making the merger decision. If managers are acting to the best interest of shareholders then they would try to increase shareholders' wealth. To solve this problem first the dynamics of mergers were analysed and then new strategies developed and demonstrated to transfer the financial synergies to the shareholders.
17
Arikan, Ali F. "Structural models for the pricing of corporate securities and financial synergies. Applications with stochastic processes including arithmetic Brownian motion." Thesis, University of Bradford, 2010. http://hdl.handle.net/10454/5416.
Full textAbstract:
Mergers are the combining of two or more firms to create synergies. These synergies
may come from various sources such as operational synergies come from
economies of scale or financial synergies come from increased value of securities
of the firm. There are vast amount of studies analysing operational synergies of
mergers. This study analyses the financial ones. This way the dynamics of purely
financial synergies can be revealed. Purely financial synergies can be transformed
into financial instruments such as securitization.
While analysing financial synergies the puzzle of distribution of financial synergies
between claimholders is investigated. Previous literature on mergers showed that
bondholders may gain more than existing shareholders of the merging firms. This
may become rather controversial. A merger may be synergistic but it does not
necessarily mean that shareholders¿ wealth will increase. Managers and/or shareholders
are the parties making the merger decision. If managers are acting to the
best interest of shareholders then they would try to increase shareholders¿ wealth.
To solve this problem first the dynamics of mergers were analysed and then new
strategies developed and demonstrated to transfer the financial synergies to the
shareholders.
18
Doshi, Ankit. "Seasonal volatility models with applications in option pricing." Gowas Publishing House, 2011. http://hdl.handle.net/1993/8889.
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GARCH models have been widely used in finance to model volatility ever since the introduction of the ARCH model and its extension to the generalized ARCH (GARCH) model. Lately, there has been growing interest in modelling seasonal volatility, most recently with the introduction of the multiplicative seasonal GARCH models.
As an application of the multiplicative seasonal GARCH model with real data, call prices from the major stock market index of India are calculated using estimated parameter values. It is shown that a multiplicative seasonal GARCH option pricing model outperforms the Black-Scholes formula and a GARCH(1,1) option pricing formula. A parametric bootstrap procedure is also employed to obtain an interval approximation of the call price. Narrower confidence intervals are obtained using the multiplicative seasonal GARCH model than the intervals provided by the GARCH(1,1) model for data that exhibits multiplicative seasonal GARCH volatility.
19
Wu, Ching-Tang. "Construction of Brownian Motions in Enlarged Filtrations and Their Role in Mathematical Models of Insider Trading." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 1999. http://dx.doi.org/10.18452/14364.
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In dieser Arbeit untersuchen wir die Struktur von Gausschen Prozessen, die durch gewisse lineare Transformationen von zwei Gausschen Martingalen erzeugt werden. Die Klasse dieser Transformationen ist durch nanzmathematische Gleichgewichtsmodelle mit heterogener Information motiviert. In Kapital 2 bestimmen wir für solche Prozesse, die zunächst in einer erweiterten Filtrierung konstruiert werden, die kanonische Zerlegung als Semimartin-gale in ihrer eigenen Filtrierung. Die resultierende Drift wird durch Volterra-Kerne beschrieben. Insbesondere charakterisieren wir diejenigen Prozesse, die in ihrer eigenen Filtrierung eine Brownsche Bewegung bilden. In Kapital 3 konstruieren wir neue orthogonale Zerlegungen der Brownschen Filtrierungen. In den Kapitaln 4 bis 6 wenden wir unsere Resultate zur Charakterisierung Brownscher Bewegungen im Kontext nanzmathematischer Modelle an, in denen es Marktteilnehmer mit zusätzlicher Insider-Information gibt. Wir untersuchen Erweiterungen eines Gleichgewichtsmodells von Kyle [42] und Back [7], in denen die Insider-Information in verschiedener Weise durch Gaussche Martingale spezifiziert wird. Insbesondere klären wir die Struktur von Insider-Strategien, die insofern unaufallig bleiben, als sich die resultierende Gesamtnachfrage wie eine Brownsche Bewegung verhält.In this thesis, we study Gaussian processes generated by certain linear transformations of two Gaussian martingales. This class of transformations is motivated by nancial equilibrium models with heterogeneous information. In Chapter 2 we derive the canonical decomposition of such processes, which are constructed in an enlarged ltration, as semimartingales in their own ltration. The resulting drift is described in terms of Volterra kernels. In particular we characterize those processes which are Brownian motions in their own ltration. In Chapter 3 we construct new orthogonal decompositions of Brownian ltrations. In Chapters 4 to 6 we are concerned with applications of our characterization results in the context of mathematical models of insider trading. We analyze extensions of the nancial equilibrium model of Kyle [42] and Back [7] where the Gaussian martingale describing the insider information is specified in various ways. In particular we discuss the structure of insider strategies which remain inconspicuous in the sense that the resulting cumulative demand is again a Brownian motion.
20
Littin, Curinao Jorge Andrés. "Quasi stationary distributions when infinity is an entrance boundary : optimal conditions for phase transition in one dimensional Ising model by Peierls argument and its consequences." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4789/document.
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Cette thèse comporte deux chapitres principaux. Deux problèmes indépendants de Modélisation Mathématique y sont étudiés. Au chapitre 1, on étudiera le problème de l’existence et de l’unicité des distributions quasi-stationnaires (DQS) pour un mouvement Brownien avec dérive, tué en zéro dans le cas où la frontière d’entrée est l’infini et la frontière de sortie est zéro selon la classification de Feller.Ce travail est lié à l’article pionnier dans ce sujet par Cattiaux, Collet, Lambert, Martínez, Méléard, San Martín; où certaines conditions suffisantes ont été établies pour prouver l’existence et l’unicité de DQS dans le contexte d’une famille de Modèles de Dynamique des Populations.Dans ce chapitre, nous généralisons les théorèmes les plus importants de ce travail pionnier, la partie technique est basée dans la théorie de Sturm-Liouville sur la demi-droite positive. Au chapitre 2, on étudiera le problème d’obtenir des bornes inférieures optimales sur l’Hamiltonien du Modèle d’Ising avec interactions à longue portée, l’interaction entre deux spins situés à distance d décroissant comme d^(2-a), où a ϵ[0,1).Ce travail est lié à l’article publié en 2005 par Cassandro, Ferrari, Merola, Presutti où les bornes inférieures optimales sont obtenues dans le cas où a est dans [0,(log3/log2)-1) en termes de structures hiérarchiques appelées triangles et contours.Les principaux théorèmes obtenus dans cette thèse peuvent être résumés de la façon suivante:1. Il n’existe pas de borne inférieure optimale pour l’Hamiltonien en termes de triangles pour a dans ϵ[log2/log3,1). 2. Il existe une borne optimale pour l’Hamiltonien en termes de contours pour a dans a ϵ [0,1)This thesis contains two main Chapters, where we study two independent problems of Mathematical Modelling : In Chapter 1, we study the existence and uniqueness of Quasi Stationary Distributions (QSD) for a drifted Browian Motion killed at zero, when $+infty$ is an entrance Boundary and zero is an exit Boundary according to Feller's classification. The work is related to the previous paper published in 2009 by { Cattiaux, P., Collet, P., Lambert, A., Martínez, S., Méléard, S., San Martín, where some sufficient conditions were provided to prove the existence and uniqueness of QSD in the context of a family of Population Dynamic Models. This work generalizes the most important theorems of this work, since no extra conditions are imposed to get the existence, uniqueness of QSD and the existence of a Yaglom limit. The technical part is based on the Sturm Liouville theory on the half line. In Chapter 2, we study the problem of getting quasi additive bounds on the Hamiltonian for the Long Range Ising Model when the interaction term decays according to d^{2-a}, a ϵ[0,1). This work is based on the previous paper written by Cassandro, Ferrari, Merola, Presutti, where quasi-additive bounds for the Hamiltonian were obtained for a in [0,(log3/log2)-1) in terms of hierarchical structures called triangles and Contours. The main theorems of this work can be summarized as follows: 1 There does not exist a quasi additive bound for the Hamiltonian in terms of triangles when a ϵ [0,(log3/log2)-1), 2. There exists a quasi additive bound for the Hamiltonian in terms of Contours for a in [0,1)
21
Antczak, Magdalena, and Marta Leniec. "Pricing and Hedging of Defaultable Models." Thesis, Högskolan i Halmstad, Tillämpad matematik och fysik (MPE-lab), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-16052.
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Modelling defaultable contingent claims has attracted a lot of interest in recent years, motivated in particular by the Late-2000s Financial Crisis. In several papers various approaches on the subject have been made. This thesis tries to summarize these results and derive explicit formulas for the prices of financial derivatives with credit risk. It is divided into two main parts. The first one is devoted to the well-known theory of modelling the default risk while the second one presents the results concerning pricing of the defaultable models that we obtained ourselves.
22
Ghorbanzadeh, Dariush. "Détection de rupture dans les modèles statistiques." Paris 7, 1992. http://www.theses.fr/1992PA077246.
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Ce travail concerne l'etude d'une classe de tests de detection de rupture dans les modeles statistiques. La classe de tests consideree est basee sur le test du rapport de vraisemblance. Dans le cadre de la contiguite au sens de lecam, sous l'hypothese nulle (non rupture) et sous l'hypothese alternative (rupture), les lois asymptotiques des statistiques de tests sont evaluees, ce qui permet de determiner asymptotiquement les regions critiques des tests. Les expressions analytiques des puissances asymptotiques sont proposees. En utilisant les techniques de l'analyse discriminante, le probleme de la detection du passage en sida avere a ete etudie par application directe sur les donnees concernant 450 patients hiv-positifs
23
Casse, Jérôme. "Automates cellulaires probabilistes et processus itérés ad libitum." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0248/document.
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La première partie de cette thèse porte sur les automates cellulaires probabilistes (ACP) sur la ligne et à deux voisins. Pour un ACP donné, nous cherchons l'ensemble de ces lois invariantes. Pour des raisons expliquées en détail dans la thèse, ceci est à l'heure actuelle inenvisageable de toutes les obtenir et nous nous concentrons, dans cette thèse, surles lois invariantes markoviennes. Nous établissons, tout d'abord, un théorème de nature algébrique qui donne des conditions nécessaires et suffisantes pour qu'un ACP admette une ou plusieurs lois invariantes markoviennes dans le cas où l'alphabet E est fini. Par la suite, nous généralisons ce résultat au cas d'un alphabet E polonais après avoir clarifié les difficultés topologiques rencontrées. Enfin, nous calculons la fonction de corrélation du modèleà 8 sommets pour certaines valeurs des paramètres du modèle en utilisant une partie desrésultats précédentsThe first part of this thesis is about probabilistic cellular automata (PCA) on the line and with two neighbors. For a given PCA, we look for the set of its invariant distributions. Due to reasons explained in detail in this thesis, it is nowadays unthinkable to get all of them and we concentrate our reections on the invariant Markovian distributions. We establish, first, an algebraic theorem that gives a necessary and sufficient condition for a PCA to have one or more invariant Markovian distributions when the alphabet E is finite. Then, we generalize this result to the case of a polish alphabet E once we have clarified the encountered topological difficulties. Finally, we calculate the 8-vertex model's correlation function for some parameters values using previous results.The second part of this thesis is about infinite iterations of stochastic processes. We establish the convergence of the finite dimensional distributions of the α-stable processes iterated n times, when n goes to infinite, according to parameter of stability and to drift r. Then, we describe the limit distributions. In the iterated Brownian motion case, we show that the limit distributions are linked with iterated functions system
24
Pain, Michel. "Mouvement brownien branchant et autres modèles hiérarchiques en physique statistique." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS305.
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Le mouvement brownien branchant (BBM) est un système de particules se déplaçant et se reproduisant aléatoirement. En premier lieu, nous étudions avec précision la transition de phase qui a lieu au sein de ce système de particules près de son minimum, en se plaçant dans le cas dit presque-critique. Ensuite, nous décrivons les fluctuations 1-stable universelles qui apparaissent dans le front du BBM, ainsi que le comportement typique des particules qui y contribuent. Une version du BBM avec sélection est également étudiée, où les particules sont tuées quand elles descendent à une distance L de la particule la plus haute : nous verrons comment cette règle de sélection affecte la vitesse de déplacement des individus les plus rapides quand L est grand. Puis, sous l'angle de la question du chaos en température pour les verres de spin, nous comparons le champ libre gaussien discret en dimension 2, un modèle possèdant une structure hiérarchique approximative et des propriétés très proches de celles du BBM, avec le Random Energy Model. Finalement, le dernier chapitre porte sur le modèle de Derrida-Retaux, qui est également défini par une structure hiérarchique. Nous introduisons une version continue de ce modèle, possédant une famille exactement soluble de solutions qui permet de répondre à différentes conjectures existantes sur le modèle discretBranching Brownian motion (BBM) is a particle system, where particles move and reproduce randomly. Firstly, we study precisely the phase transition occuring for this particle system close to its minimum, in the setting of the so-called near-critical case. Then, we describe the universal 1-stable fluctuations appearing in the front of BBM and identify the typical behavior of particles contributing to them. A version of BBM with selection, where particles are killed when going down at a distance larger than L from the highest particle, is also sudied: we see how this selection rule affects the speed of the fastest individuals in the population, when L is large. Thereafter, motivated by temperature chaos in spin glasses, we study the 2-dimensional discrete Gaussian free field, which is a model with an approximative hierarchical structure and properties similar to BBM, and show that, from this perspective, it behaves differently than the Random Energy Model. Finally, the last part of this thesis is dedicated to the Derrida-Retaux model, which is also defined by a hierarchical structure. We introduce a continuous time version of this model and exhibit a family of exactly solvable solutions, which allows us to answer several conjectures stated on the discrete time model
25
Coulon, Jérôme. "Mémoire longue, volatilité et gestion de portefeuille." Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00657711.
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Cette thèse porte sur l'étude de la mémoire longue de la volatilité des rendements d'actions. Dans une première partie, nous apportons une interprétation de la mémoire longue en termes de comportement d'agents grâce à un modèle de volatilité à mémoire longue dont les paramètres sont reliés aux comportements hétérogènes des agents pouvant être rationnels ou à rationalité limitée. Nous déterminons de manière théorique les conditions nécessaires à l'obtention de mémoire longue. Puis nous calibrons notre modèle à partir des séries de volatilité réalisée journalière d'actions américaines de moyennes et grandes capitalisations et observons le changement de comportement des agents entre la période précédant l'éclatement de la bulle internet et celle qui la suit. La deuxième partie est consacrée à la prise en compte de la mémoire longue en gestion de portefeuille. Nous commençons par proposer un modèle de choix de portefeuille à volatilité stochastique dans lequel la dynamique de la log-volatilité est caractérisée par un processus d'Ornstein-Uhlenbeck. Nous montrons que l'augmentation du niveau d'incertitude sur la volatilité future induit une révision du plan de consommation et d'investissement. Puis dans un deuxième modèle, nous introduisons la mémoire longue grâce au mouvement brownien fractionnaire. Cela a pour conséquence de transposer le système économique d'un cadre markovien à un cadre non-markovien. Nous fournissons donc une nouvelle méthode de résolution fondée sur la technique de Monte Carlo. Puis, nous montrons toute l'importance de modéliser correctement la volatilité et mettons en garde le gérant de portefeuille contre les erreurs de spécification de modèle.
26
Manzini, Muzi Charles. "Stochastic Volatility Models for Contingent Claim Pricing and Hedging." Thesis, University of the Western Cape, 2008. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_8197_1270517076.
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The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo
smile&rdquo
curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.
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Rings, Daniel. "Hot Brownian Motion." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-102186.
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The theory of Brownian motion is a cornerstone of modern physics. In this thesis, we introduce a nonequilibrium extension to this theory, namely an effective Markovian theory of the Brownian motion of a heated nanoparticle. This phenomenon belongs to the class of nonequilibrium steady states (NESS) and is characterized by spatially inhomogeneous temperature and viscosity fields extending in the solvent surrounding the nanoparticle.
The first chapter provides a pedagogic introduction to the subject and a concise summary of our main results and summarizes their implications for future developments and innovative applications.
The derivation of our main results is based on the theory of fluctuating hydrodynamics, which we introduce and extend to NESS conditions, in the second chapter. We derive the effective temperature and the effective friction coefficient for the generalized Langevin equation describing the Brownian motion of a heated nanoparticle. As major results, we find that these parameters obey a generalized Stokes–Einstein relation, and that, to first order in the temperature increment of the particle, the effective temperature is given in terms of a set of universal numbers.
In chapters three and four, these basic results are made explicit for various realizations of hot Brownian motion. We show in detail, that different degrees of freedom are governed by distinct effective parameters, and we calculate these for the rotational and translational motion of heated nanobeads and nanorods. Whenever possible, analytic results are provided, and numerically accurate approximation methods are devised otherwise.
To test and validate all our theoretical predictions, we present large-scale molecular dynamics simulations of a Lennard-Jones system, in chapter five. These implement a state-of-the-art GPU-powered parallel algorithm, contributed by D. Chakraborty. Further support for our theory comes from recent experimental observations of gold nanobeads and nanorods made in the the groups of F. Cichos and M. Orrit. We introduce the theoretical concept of PhoCS, an innovative technique which puts the selective heating of nanoscopic tracer particles to good use.
We conclude in chapter six with some preliminary results about the self-phoretic motion of so-called Janus particles. These two-faced hybrids with a hotter and a cooler side perform a persistent random walk with the persistence only limited by their hot rotational Brownian motion. Such particles could act as versatile laser-controlled nanotransporters or nanomachines, to mention just the most obvious future nanotechnological applications of hot Brownian motion.
28
Rings, Daniel, Romy Radünz, Frank Cichos, and Klaus Kroy. "Hot brownian motion." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-190908.
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Rings, Daniel, Romy Radünz, Frank Cichos, and Klaus Kroy. "Hot brownian motion." Diffusion fundamentals 11 (2009) 75, S. 1-2, 2009. https://ul.qucosa.de/id/qucosa%3A14040.
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Trefán, György. "Deterministic Brownian Motion." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc279262/.
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The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscpoic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism - the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-Planck equation rests on the Central Limit Theorem, and, consequently, on the possibility of deriving it from a deterministic process with a quickly decaying correlation function. The sensitive dependence on initial conditions, one of the defining properties of chaos insures this rapid decay. We carefully address the problem of deriving dissipation from the interaction of a particle with a fully deterministic nonlinear bath, that we term the booster. We show that the solution of this problem essentially rests on the linear response of a booster to an external perturbation. This raises a long-standing problem concerned with Kubo's Linear Response Theory and the strong criticism against it by van Kampen. Kubo's theory is based on a perturbation treatment of the Liouville equation, which, in turn, is expected to be totally equivalent to a first-order perturbation treatment of single trajectories. Since the boosters are chaotic, and chaos is essential to generate diffusion, the single trajectories are highly unstable and do not respond linearly to weak external perturbation. We adopt chaotic maps as boosters of a Brownian particle, and therefore address the problem of the response of a chaotic booster to an external perturbation. We notice that a fully chaotic map is characterized by an invariant measure which is a continuous function of the control parameters of the map. Consequently if the external perturbation is made to act on a control parameter of the map, we show that the booster distribution undergoes slight modifications as an effect of the weak external perturbation, thereby leading to a linear response of the mean value of the perturbed variable of the booster. This approach to linear response completely bypasses the criticism of van Kampen. The joint use of these two phenomena, diffusion and friction stemming from the interaction of the Brownian particle with the same booster, makes the microscopic derivation of a Fokker-Planck equation and Brownian motion, possible.
31
Hobson, Tim. "Slowly-coalescing Brownian motion." Thesis, University of Warwick, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.487910.
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An interacting particle system is constructed in which a collection of independent Brownian motions are subject to the rule that each pair of particles shall coalesce at a rate given formally by ). dLt , where {Lt : t ~ O} is the intersection local time of the pair. This interaction mechanism is referred to as slowly-coalescing, in contrast to the more standard model in which particles coalesce immediately on collision. The process is shown to be the weak limit of a sequence of coalescing symmeteric random walks on the lattice n-1Z. Our indirect argument exploits the existence of a dual Markov process at both the discrete and the continuous level. By endowing each of the slowly-coalescing Brownian particles with a weight we are able to establish a more intimate duality, the dual process being the solution of a stochastic heat equation driven by Fisher-Wright noise.
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Allez, Romain. "Chaos multiplicatif Gaussien, matrices aléatoires et applications." Phd thesis, Université Paris Dauphine - Paris IX, 2012. http://tel.archives-ouvertes.fr/tel-00780270.
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Dans ce travail, nous nous sommes intéressés d'une part à la théorie du chaos multiplicatif Gaussien introduite par Kahane en 1985 et d'autre part à la théorie des matrices aléatoires dont les pionniers sont Wigner, Wishart et Dyson. La première partie de ce manuscrit contient une brève introduction à ces deux théories ainsi que les contributions personnelles de ce manuscrit expliquées rapidement. Les parties suivantes contiennent les textes des articles publiés [1], [2], [3], [4], [5] et pré-publiés [6], [7], [8] sur ces résultats dans lesquels le lecteur pourra trouver des développements plus détaillés
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Menes, Matheus Dorival Leonardo Bombonato. "Versão discreta do modelo de elasticidade constante da variância." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-16042013-151325/.
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Neste trabalho propomos um modelo de mercado através de uma discretização aleatória do movimento browniano proposta por Leão & Ohashi (2010). Com este modelo, dada uma função payoff, vamos desenvolver uma estratégia de hedging e uma metodologia para precificação de opçõesIn this work we propose a market model using a discretization scheme of the random Brownian motion proposed by Leão & Ohashi (2010). With this model, for any given payoff function, we develop a hedging strategy and a methodology to option pricing
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Mather, William Hardeman. "Rectified Brownian Motion in Biology." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16244.
Full textAbstract:
Nanoscale biological systems operate in the presence of overwhelming viscous drag and thermal diffusion, thus invalidating the use of macroscopically oriented thinking to explain such systems. Rectified Brownian motion (RBM), in contrast, is a distinctly nanoscale approach that thrives in thermal environments. The thesis discusses both the foundations and applications of RBM, with an emphasis on nano-biology. Results from stochastic non-equilibrium steady state theory are used to motivate a compelling definition for RBM. It follows that RBM is distinct from both the so-called power stroke and Brownian ratchet approaches to nanoscale mechanisms. Several physical examples provide a concrete foundation for these theoretical arguments. Notably, the molecular motors kinesin and myosin V are proposed to function by means of a novel RBM mechanism: strain-induced bias amplification. The conclusion is reached that RBM is a versatile and robust approach to nanoscale biology.
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Neves, Susana de Matos. "Fractional Brownian Motion in Finance." Master's thesis, Instituto Superior de Economia e Gestão, 2012. http://hdl.handle.net/10400.5/10326.
Full textAbstract:
Mestrado em Matemática FinanceiraAlgumas das propriedades estatísticas dos dados financeiros são comuns a uma ampla variedade de mercados: a propriedade de memória longa, as caudas pesadas, assimetria (ganho / perda de assimetria), saltos, agrupamento de volatilidade, etc. A necessidade de procurar novos modelos de produtos financeiros tem aumentado nas últimas décadas devido à incapacidade dos actuais modelos explicarem algumas dessas propriedades estatísticas. Este trabalho tem como objetivo dar uma visão geral de alguns estudos que foram feitos relativamente à aplicação às finanças do movimento Browniano fracionário, em particular o trabalho de Paolo Guasoni e Cheridito Patrick, que mostram que, se assumirmos certas restrições, podemos eliminar oportunidades de arbitragem. Além disso, também são apresentados estudos empíricos com dados de mercado, com o objectivo de mostrar como se pode obter um estimador para o índice Hurst (o parâmetro do movimento Browniano fracionário). Para este fim, foram utilizados dois métodos, o método Rescaled Range e o método modificado do Rescaled Range. Este estudo permite-nos discutir o efeito de memória nas séries temporais de alguns índices de mercado.
Some of the statistical properties of the financial data are common to a wide variety of markets: long-range dependence properties, heavy tails, skewness (gain/loss asymmetry), jumps, volatility clustering, etc. The need to seek new models for financial products has increased in recent decades due to the inability of current models to explain some of these facts. One of these models is fractional Brownian motion. This work aims to give an overview of some studies that were done on the financial applications of fractional Brownian motion, in particular the work of Paolo Guasoni and Patrick Cheridito which shows that if we assume certain restrictions, we can eliminate arbitrage opportunities. Moreover, we also present empirical studies with market data, in order to show how to obtain an estimator for the Hurst index (the fractional Brownian motion parameter). To this end, we used two methods, the Rescaled Range Analysis and the modified Rescaled Range Analysis. This study allows us to discuss the effect of memory on the time series of some market indices.
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Inkaya, Alper. "Option Pricing With Fractional Brownian Motion." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613736/index.pdf.
Full textAbstract:
Traditional financial modeling is based on semimartingale processes with stationary and independent
increments. However, empirical investigations on financial data does not always
support these assumptions. This contradiction showed that there is a need for new stochastic
models. Fractional Brownian motion (fBm) was proposed as one of these models by Benoit
Mandelbrot. FBm is the only continuous Gaussian process with dependent increments. Correlation
between increments of a fBm changes according to its self-similarity parameter H. This
property of fBm helps to capture the correlation dynamics of the data and consequently obtain
better forecast results. But for values of H different than 1/2, fBm is not a semimartingale and
classical Ito formula does not exist in that case. This gives rise to need for using the white noise
theory to construct integrals with respect to fBm and obtain fractional Ito formulas. In this
thesis, the representation of fBm and its fundamental properties are examined. Construction of
Wick-Ito-Skorohod (WIS) and fractional WIS integrals are investigated. An Ito type formula
and Girsanov type theorems are stated. The financial applications of fBm are mentioned and
the Black&Scholes price of a European call option on an asset which is assumed to follow a geometric fBm is derived. The statistical aspects of fBm are investigated. Estimators for the self-similarity parameter H and simulation methods of fBm are summarized. Using the R/S methodology of Hurst, the estimations of the parameter H are obtained and these values are used to evaluate the fractional Black&
Scholes prices of a European call option with different maturities. Afterwards, these values are compared to Black&
Scholes price of the same option to demonstrate the effect of long-range dependence on the option prices. Also, estimations of H at different time scales are obtained to investigate the multiscaling in financial data. An outlook of the future work is given.
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Howitt, Christopher John. "Stochastic flows and sticky Brownian motion." Thesis, University of Warwick, 2007. http://wrap.warwick.ac.uk/56226/.
Full textAbstract:
Sticky Brownian motion is a one-dimensional diffusion with the property that the amount of time the process spends at zero is of positive Lebesgue measure and yet the process does not stay at zero for any positive interval of time. Sticky Brownian motion can be considered as qualitatively between standard Brownian motion and Brownian motion absorbed at zero. A system of coalescing Brownian motions is a collection of paths, where each path behaves as a Brownian motion independent of all other paths until the first time two paths meet, at which point the two paths that have just met behave is a single Brownian motion independent of all remaining paths. Thus the difference between any two paths of a system of coalescing Brownian motion behaves as a Brownian motion absorbed at zero. In this thesis we consider systems of Brownian paths, where the difference between any two paths behaves as a sticky Brownian motion rather than a coalescing Brownian motion. We consider systems of sticky Brownian motions starting from points in continuous time and space. The evolution of systems of this type may be described by means of a stochastic flow of kernels. A stochastic flow of kernels is characterised by its N-point motions which form a consistent family of Brownian motions. We characterise such a consistent family such that the difference between any pair of coordinates behaves as a sticky Brownian motion. The Brownian web is a way of describing a system of coalescing Brownian motions starting in any point in space and time. We describe a coupling of Brownian webs such that the difference between one path in each web behaves as a sticky Brownian motion. Then by conditioning one Brownian web on the other we can construct a stochastic flow of kernels. Finally we discuss the concept of duality in relation to flows and we prove some minor results relating to these dualities.
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Bechinger, Clemens. "Active Brownian motion of asymmetric particles." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-179545.
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Grebenkov, Denis S. "Residence times of reflected brownian motion." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-193387.
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Lessa, Pablo. "Brownian motion on stationary random manifolds." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2014. http://tel.archives-ouvertes.fr/tel-00959923.
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On introduit le concept d'une variété aléatoire stationnaire avec l'objectif de traiter de façon unifiée les résultats sur les variétés avec un group d'isométries transitif, les variétés avec quotient compact, et les feuilles génériques d'un feuilletage compact. On démontre des inégalités entre la vitesse de fuite, l'entropie du mouvement brownien et la croissance de volume de la variété aléatoire, en généralisant des résultats d'Avez, Kaimanovich, et Ledrappier. Dans la deuxième partie on démontre que la fonction feuille d'un feuilletage compact est semicontinue, en obtenant comme conséquences le théorème de stabilité local de Reeb, une partie du théorème de structure local pour les feuilletages à feuilles compactes d'Epstein, et un théorème de continuité d'Álvarez et Candel.
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Dunkel, Jörn. "Relativistic Brownian motion and diffusion processes." kostenfrei, 2008. http://d-nb.info/991318757/34.
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Jehring, Kristin Elizabeth. "Harmonic functions on Walsh's Brownian motion." Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3355766.
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Thesis (Ph. D.)--University of California, San Diego, 2009.Title from first page of PDF file (viewed June 25, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 82-83).
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Grebenkov, Denis S. "Residence times of reflected brownian motion." Diffusion fundamentals 6 (2007) 21, S. 1-2, 2007. https://ul.qucosa.de/id/qucosa%3A14195.
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Bechinger, Clemens. "Active Brownian motion of asymmetric particles." Diffusion fundamentals 20 (2013) 16, S. 1, 2013. https://ul.qucosa.de/id/qucosa%3A13540.
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Lampo, Aniello, Soon Hoe Lim, Jan Wehr, Pietro Massignan, and Maciej Lewenstein. "Lindblad model of quantum Brownian motion." AMER PHYSICAL SOC, 2016. http://hdl.handle.net/10150/622483.
Full textAbstract:
The theory of quantum Brownian motion describes the properties of a large class of open quantum systems. Nonetheless, its description in terms of a Born-Markov master equation, widely used in the literature, is known to violate the positivity of the density operator at very low temperatures. We study an extension of existing models, leading to an equation in the Lindblad form, which is free of this problem. We study the dynamics of the model, including the detailed properties of its stationary solution, for both constant and position-dependent coupling of the Brownian particle to the bath, focusing in particular on the correlations and the squeezing of the probability distribution induced by the environment.
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Lange, Rutger-Jan. "Brownian motion and multidimensional decision making." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/243402.
Full textAbstract:
This thesis consists of three self-contained parts, each with its own abstract, body, references and page numbering. Part I, 'Potential theory, path integrals and the Laplacian of the indicator', finds the transition density of absorbed or reflected Brownian motion in a d-dimensional domain as a Feynman-Kac functional involving the Laplacian of the indicator, thereby relating the hitherto unrelated fields of classical potential theory and path integrals. Part II, 'The problem of alternatives', considers parallel investment in alternative technologies or drugs developed over time, where there can be only one winner. Parallel investment accelerates the search for the winner, and increases the winner's expected performance, but is also costly. To determine which candidates show sufficient performance and/or promise, we find an integral equation for the boundary of the optimal continuation region. Part III, 'Optimal support for renewable deployment', considers the role of government subsidies for renewable technologies. Rapidly diminishing subsidies are cheaper for taxpayers, but could prematurely kill otherwise successful technologies. By contrast, high subsidies are not only expensive but can also prop up uneconomical technologies. To analyse this trade-off we present a new model for technology learning that makes capacity expansion endogenous. There are two reasons for this standalone structure. First, the target readership is divergent. Part I concerns mathematical physics, Part II operations research, and Part III policy. Readers interested in specific parts can thus read these in isolation. Those interested in the thesis as a whole may prefer to read the three introductions first. Second, the separate parts are only partially interconnected. Each uses some theory from the preceding part, but not all of it; e.g. Part II uses only a subset of the theory from Part I. The quickest route to Part III is therefore not through the entirety of the preceding parts. Furthermore, those instances where results from previous parts are used are clearly indicated.
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Mota, Pedro José dos Santos Palhinhas. "Brownian motion with drift threshold model." Doctoral thesis, FCT - UNL, 2008. http://hdl.handle.net/10362/1766.
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In this thesis we implement estimating procedures in order to estimate threshold
parameters for the continuous time threshold models driven by stochastic di®erential
equations. The ¯rst procedure is based on the EM (expectation-maximization) algorithm
applied to the threshold model built from the Brownian motion with drift process. The
second procedure mimics one of the fundamental ideas in the estimation of the thresholds
in time series context, that is, conditional least squares estimation. We implement this
procedure not only for the threshold model built from the Brownian motion with drift
process but also for more generic models as the ones built from the geometric Brownian
motion or the Ornstein-Uhlenbeck process. Both procedures are implemented for simu-
lated data and the least squares estimation procedure is also implemented for real data
of daily prices from a set of international funds. The ¯rst fund is the PF-European Sus-
tainable Equities-R fund from the Pictet Funds company and the second is the Parvest
Europe Dynamic Growth fund from the BNP Paribas company. The data for both funds
are daily prices from the year 2004. The last fund to be considered is the Converging
Europe Bond fund from the Schroder company and the data are daily prices from the
year 2005.European Community's Human Po-tential Programme under contract HPRN-CT-2000-00100, DYNSTOCH and by PRODEP III (medida 5 - Acção 5.3)
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Fauth, Alexis. "Contributions à la modélisation des données financières à hautes fréquences." Thesis, Paris 1, 2014. http://www.theses.fr/2014PA010019.
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Cette thèse a été réalisée au sein de l’entreprise Invivoo. L’objectif principal était de trouver des stratégies d’investissement : avoir un gain important et un risque faible. Les travaux de recherche ont été principalement portés par ce dernier point. Dans ce sens, nous avons voulu généraliser un modèle fidèle à la réalité des marchés financiers, que ce soit pour des données à basse comme à haute fréquence et, à très haute fréquence, variation par variationNo English summary available
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Bruna, Maria. "Excluded-volume effects in stochastic models of diffusion." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:020c2d3e-5fef-478c-9861-553cd310daf5.
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Stochastic models describing how interacting individuals give rise to collective behaviour have become a widely used tool across disciplines—ranging from biology to physics to social sciences. Continuum population-level models based on partial differential equations for the population density can be a very useful tool (when, for large systems, particle-based models become computationally intractable), but the challenge is to predict the correct macroscopic description of the key attributes at the particle level (such as interactions between individuals and evolution rules). In this thesis we consider the simple class of models consisting of diffusive particles with short-range interactions. It is relevant to many applications, such as colloidal systems and granular gases, and also for more complex systems such as diffusion through ion channels, biological cell populations and animal swarms. To derive the macroscopic model of such systems, previous studies have used ad hoc closure approximations, often generating errors. Instead, we provide a new systematic method based on matched asymptotic expansions to establish the link between the individual- and the population-level models. We begin by deriving the population-level model of a system of identical Brownian hard spheres. The result is a nonlinear diffusion equation for the one-particle density function with excluded-volume effects enhancing the overall collective diffusion rate. We then expand this core problem in several directions. First, for a system with two types of particles (two species) we obtain a nonlinear cross-diffusion model. This model captures both alternative notions of diffusion, the collective diffusion and the self-diffusion, and can be used to study diffusion through obstacles. Second, we study the diffusion of finite-size particles through confined domains such as a narrow channel or a Hele–Shaw cell. In this case the macroscopic model depends on a confinement parameter and interpolates between severe confinement (e.g., a single- file diffusion in the narrow channel case) and an unconfined situation. Finally, the analysis for diffusive soft spheres, particles with soft-core repulsive potentials, yields an interaction-dependent non-linear term in the diffusion equation.
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Serrano, Francisco de Castilho Monteiro Gil. "Fractional processes: an application to finance." Master's thesis, Instituto Superior de Economia e Gestão, 2016. http://hdl.handle.net/10400.5/13002.
Full textAbstract:
Mestrado em Matemática FinanceiraNeste trabalho é apresentada uma extensa descrição matemática, orientada para a modelação financeira, de três principais processos fracionários: o processo Browniano fracionário e os dois processos de Lévy fracionários. Mostram-se como estes processos podem ser originados. É explorado o conceito de auto-semelhança e apresentamos algumas noções de cálculo fracionário. Também é discutido o lugar destes processos no problema de encontrar o preço de derivados financeiros e apresentamos uma nova abordagem para a simulação do processo de Lévy fracionário que permite um método Monte Carlo para encontrar o preço de derivados financeiros.
In this work it is presented an extensive mathematical description oriented to financial modelling based on three main fractional processes: the fractional Brownian motion and both fractional Lévy processes. It is shown how these processes were originated. The concept of self-similarity is explored and we present some notions of fractional calculus. It is discussed the opportunity of these processes in pricing financial derivatives and we present a new approach for simulation of the fractional Lévy process, which allows a Monte Carlo method for pricing financial derivatives.
info:eu-repo/semantics/publishedVersion