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Dissertations / Theses on the topic 'Stochastic Delay Differential Equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Bahar, Arifah. "Applications of stochastic differential equations and stochastic delay differential equations in population dynamics." Thesis, University of Strathclyde, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415294.

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2

Reiss, Markus. "Nonparametric estimation for stochastic delay differential equations." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964782480.

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3

Reiß, Markus. "Nonparametric estimation for stochastic delay differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2002. http://dx.doi.org/10.18452/14741.

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Sei (X(t), t>= -r) ein stationärer stochastischer Prozess, der die affine stochastische Differentialgleichung mit Gedächtnis dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, löst, wobei sigma>0, (W(t), t>=0) eine Standard-Brownsche Bewegung und L ein stetiges lineares Funktional auf dem Raum der stetigen Funktionen auf [-r,0], dargestellt durch ein endliches signiertes Maß a, bezeichnet. Wir nehmen an, dass eine Trajektorie (X(t), -r 0, konvergiert. Diese Rate ist schlechter als in vielen klassischen Fällen. Wir beweisen jedoch eine untere Schranke, die zeigt, dass keine Schätzung eine bessere Rate im Mi

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4

Guillouzic, Steve. "Fokker-Planck approach to stochastic delay differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58279.pdf.

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5

René, Alexandre. "Spectral Solution Method for Distributed Delay Stochastic Differential Equations." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34327.

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Stochastic delay differential equations naturally arise in models of complex natural phenomena, yet continue to resist efforts to find analytical solutions to them: general solutions are limited to linear systems with additive noise and a single delayed term. In this work we solve the case of distributed delays in linear systems with additive noise. Key to our solution is the development of a consistent interpretation for integrals over stochastic variables, obtained by means of a virtual discretization procedure. This procedure makes no assumption on the form of noise, and would likely be use

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6

Zhuang, Dawei. "Stability analysis of stochastic differential delay equations with jumps." Thesis, Swansea University, 2011. https://cronfa.swan.ac.uk/Record/cronfa42955.

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7

McDaniel, Austin James. "The Effects of Time Delay on Noisy Systems." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/556867.

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We consider a general stochastic differential delay equation (SDDE) with multiplicative colored noise. We study the limit as the time delays and the correlation times of the noises go to zero at the same rate. First, we derive the limiting equation for the equation obtained by Taylor expanding the SDDE to first order in the time delays. The limiting equation contains a noise-induced drift term that depends on the ratios of the time delays to the correlation times of the noises. We prove that, under appropriate assumptions, the solution of the equation obtained by the Taylor expansion converges

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8

Norton, Stewart J. "Noise induced changes to dynamic behaviour of stochastic delay differential equations." Thesis, University of Chester, 2008. http://hdl.handle.net/10034/72780.

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9

Kinnally, Michael Sean. "Stationary distributions for stochastic delay differential equations with non-negativity constraints." Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3355747.

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Thesis (Ph. D.)--University of California, San Diego, 2009.<br>Title from first page of PDF file (viewed June 23, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 114-116).

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10

McWilliams, Nairn Anthony. "Option pricing techniques under stochastic delay models." Thesis, University of Edinburgh, 2011. http://hdl.handle.net/1842/5754.

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The Black-Scholes model and corresponding option pricing formula has led to a wide and extensive industry, used by financial institutions and investors to speculate on market trends or to control their level of risk from other investments. From the formation of the Chicago Board Options Exchange in 1973, the nature of options contracts available today has grown dramatically from the single-date contracts considered by Black and Scholes (1973) to a wider and more exotic range of derivatives. These include American options, which can be exercised at any time up to maturity, as well as options ba

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11

Altemeier, Daniel [Verfasser], and Barbara [Akademischer Betreuer] Gentz. "Concentration Inequalities for Nonautonomous Stochastic Delay Differential Equations / Daniel Altemeier ; Betreuer: Barbara Gentz." Bielefeld : Universitätsbibliothek Bielefeld, 2017. http://d-nb.info/1150182024/34.

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12

Wang, C. "On asymptotic stability of stochastic differential equations with delay in infinite dimensional spaces." Thesis, University of Liverpool, 2017. http://livrepository.liverpool.ac.uk/3007651/.

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In most stochastic dynamical systems which describe process in engineering, physics and economics, stochastic components and random noise are often involved. Stochastic effects of these models are often used to capture the uncertainty about the operating systems. Motivated by the development of analysis and theory of stochastic processes, as well as the studies of natural sciences, the theory of stochastic differential equations in infinite dimensional spaces evolves gradually into a branch of modern analysis. In the analysis of such systems, we want to investigate their stabilities. This thes

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13

Stok, Roberto. "Estimation of railway capacity consumption using stochastic differential equations." Doctoral thesis, Università degli studi di Trieste, 2008. http://hdl.handle.net/10077/2753.

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2006/2007<br>The efficient utilization of railway infrastructures is a primary objective in an open-market context like the European one. The capacity consumption, that is the infrastructure occupation augmented with buffers to avoid delays (referred to a time window, e.g. peak hour or day), is a measure of the utilization level of a given timetable. The standard UIC leaflet "Capacity" recommends a procedure to evaluate the infrastructure occupation, without buffers, by compressing the timetable until the blocking time stairways touch each other in the critical section. There is no recommendat

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14

Lorenz, Robert. "Weak approximation of stochastic delay differential equations with bounded memory by discrete time series." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980367433.

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15

Wang, Yong Tian. "Stochastic differential delay equation with jumps and application to finance." Thesis, Swansea University, 2007. https://cronfa.swan.ac.uk/Record/cronfa43121.

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16

Lorenz, Robert. "Weak approxamation of stochastic delay." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2006. http://dx.doi.org/10.18452/15488.

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Wir betrachten die stochastische Differentialgleichung mit Gedächtnis (SDDE) mit Gedächtnislänge r dX(t) = b(X(u);u in [t-r,t])dt + sigma(X(u);u in [t-r,t])dB(t) mit eindeutiger schwacher Lösung. Dabei ist B eine Brownsche Bewegung, b and sigma sind stetige, lokal beschränkte Funktionen mit Definitionsbereich C[-r,0], und X(u);u in [t-r,t] bezeichnet das Segment der Werte von X(u) für Zeitpunkte u im Intervall [t,t-r]. Unser Ziel ist eine Folge von diskreten Zeitreihen Xh höherer Ordung zu konstruieren, so dass mit h gegen 0 die Zeitreihen Xh schwach gegen die Lösung X der stoch

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17

Kemajou, Elisabeth. "A Stochastic Delay Model for Pricing Corporate Liabilities." OpenSIUC, 2012. https://opensiuc.lib.siu.edu/dissertations/547.

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We suppose that the price of a firm follows a nonlinear stochastic delay differential equation. We also assume that any claim whose value depends on firm value and time follows a nonlinear stochastic delay differential equation. Using self-financed strategy and replication we are able to derive a random partial differential equation (RPDE) satisfied by any corporate claim whose value is a function of firm value and time. Under specific final and boundary conditions, we solve the RPDE for the debt value and loan guarantees within a single period and homogeneous class of debt. We then analyze th

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18

Pleis, Jan [Verfasser], Andreas [Akademischer Betreuer] Rößler, and Andreas [Akademischer Betreuer] Neuenkirch. "Lp and pathwise convergence of the Milstein scheme for stochastic delay differential equations / Jan Pleis ; Akademische Betreuer: Andreas Rößler, Andreas Neuenkirch." Lübeck : Zentrale Hochschulbibliothek Lübeck, 2021. http://d-nb.info/122492598X/34.

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19

Kumar, Chaman. "Explicit numerical schemes of SDEs driven by Lévy noise with super-linear coeffcients and their application to delay equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/15946.

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We investigate an explicit tamed Euler scheme of stochastic differential equation with random coefficients driven by Lévy noise, which has super-linear drift coefficient. The strong convergence property of the tamed Euler scheme is proved when drift coefficient satisfies one-sided local Lipschitz condition whereas diffusion and jump coefficients satisfy local Lipschitz conditions. A rate of convergence for the tamed Euler scheme is recovered when local Lipschitz conditions are replaced by global Lipschitz conditions and drift satisfies polynomial Lipschitz condition. These findings are consist

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20

Zhang, Jianing. "Non-standard backward stochastic differential equations and multiple optimal stopping problems with applications to securities pricing." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16713.

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Zentraler Gegenstand dieser Dissertation ist die Entwicklung von mathematischen Methoden zur Charakterisierung und Implementierung von optimalen Investmentstrategien eines Kleininvestors auf einem Finanzmarkt. Zur Behandlung dieser Probleme ziehen wir als Hauptwerkzeug Stochastische Rückwärts-Differenzialgleichungen (BSDEs) mit nicht-linearen Drifts heran. Diese Nicht-Lineariäten ordnen sie außerhalb der Standardklasse der Lipschitz-stetigen BSDEs ein und treten häufig in finanzmathematischen Kontrollproblemen auf. Wir charakterisieren das optimale Vermögen und die optimale Investmentstrategie

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21

Shabala, Alexander. "Mathematical modelling of oncolytic virotherapy." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:cca2c9bc-cbd4-4651-9b59-8a4dea7245d1.

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This thesis is concerned with mathematical modelling of oncolytic virotherapy: the use of genetically modified viruses to selectively spread, replicate and destroy cancerous cells in solid tumours. Traditional spatially-dependent modelling approaches have previously assumed that virus spread is due to viral diffusion in solid tumours, and also neglect the time delay introduced by the lytic cycle for viral replication within host cells. A deterministic, age-structured reaction-diffusion model is developed for the spatially-dependent interactions of uninfected cells, infected cells and virus par

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22

Lessard, Jean-Philippe. "Validated Continuation for Infinite Dimensional Problems." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19861.

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Studying the zeros of a parameter dependent operator F defined on a Hilbert space H is a fundamental problem in mathematics. When the Hilbert space is finite dimensional, continuation provides, via predictor-corrector algorithms, efficient techniques to numerically follow the zeros of F as we move the parameter. In the case of infinite dimensional Hilbert spaces, this procedure must be applied to some finite dimensional approximation which of course raises the question of validity of the output. We introduce a new technique that combines the information obtained from the predictor-corrector st

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23

Riedle, Markus. "Stochastische Differentialgleichungen mit unendlichem Gedächtnis." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2003. http://dx.doi.org/10.18452/14931.

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Für einen R^d-wertigen stochastischen Prozess X auf R bezeichne X_t den Segmentprozess X_t:={X(t+u): u = 0. Es wird folgende affine stochastische Differentialgleichung mit unendlichem Gedächtnis betrachtet: dX(t)=L(X_t)dt + dW(t) für t >= 0, X_0=F, (A) wobei L:B -> R^d ein lineares stetiges Funktional, W einen Wiener-Prozess mit Werten in R^d sowie B einen semi-normierten linearen Unterraum von {f:(-00, 0] -> R^d} bezeichnen. Die Anfangsbedingung F ist eine B-wertige Zufallsvariable. Die Lösung X der Gleichung (A) lässt sich mittels einer Formel der Variation der Konstanten darste

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24

NOTARANGELO, Girolama. "Asymptotic mean-square stability analysis and simulations of a stochastic model for the human immune response with memory." Doctoral thesis, Università degli studi di Ferrara, 2011. http://hdl.handle.net/11392/2388820.

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In this thesis we extended a deterministic model for the Human Immune response, consisting of a non-linear system of differential equations with distributed time delay, which was introduced by Beretta, Kirshner and Marino in 2007, by incorporating stochastic perturbations with multiplicative noise around equilibria of the deterministic model. Our aim is to study the robustness of the equilibria of the deterministic model for the human immune response system with respect to fluctuations due to considering the human body as a noisy enviroment. We do this by analysing the asymptotic mean square s

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25

Berntson, B. K. "Integrable delay-differential equations." Thesis, University College London (University of London), 2017. http://discovery.ucl.ac.uk/1566618/.

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Delay-differential equations are differential-difference equations in which the derivatives and shifts are taken with respect to the same variable. This thesis is concerned with these equations from the perspective of the theory of integrable systems, and more specifically, Painlevé equations. Both the classical Painlevé equations and their discrete analogues can be obtained as deautonomizations of equations solved by two-parameter families of elliptic functions. In analogy with this paradigm, we consider autonomous delay-differential equations solved by elliptic functions, delay-differentia

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26

Allen, Brenda. "Non-smooth differential delay equations." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390472.

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27

Dareiotis, Anastasios Constantinos. "Stochastic partial differential and integro-differential equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/14186.

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In this work we present some new results concerning stochastic partial differential and integro-differential equations (SPDEs and SPIDEs) that appear in non-linear filtering. We prove existence and uniqueness of solutions of SPIDEs, we give a comparison principle and we suggest an approximation scheme for the non-local integral operators. Regarding SPDEs, we use techniques motivated by the work of De Giorgi, Nash, and Moser, in order to derive global and local supremum estimates, and a weak Harnack inequality.

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28

Abourashchi, Niloufar. "Stability of stochastic differential equations." Thesis, University of Leeds, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509828.

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29

Fontana, Gaia. "Traffic waves and delay differential equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21211/.

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Questo elaborato si pone l'obiettivo di studiare il problema del traffico, concentrandosi su un modello semplificato in cui i veicoli sono confinati su una circonferenza e la cui velocità è determinata dal modello optimal velocity. Il discorso si sviluppa su tre capitoli: nel primo viene presentato il modello optimal velocity per il flusso del traffico e si procede a uno studio della stabilità lineare attorno al punto di equilibrio stazionario. Nel secondo capitolo lo stesso modello viene studiato nel limite termodinamico per un numero infinito di veicoli. Si ricava una soluzione costituita

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30

Taylor, S. Richard. "Probabilistic Properties of Delay Differential Equations." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1183.

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Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, <em>i. e. </em> in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the dynamics of ensembles (statistical mechanics) and systems with uncertainty in the initial conditions. It is also the basis of ergodic theory--the study of probabilistic invariants of dynamical systems--which provides one framework for understanding chaotic systems whose time evolutions are erratic and for practical purposes unpredictable.

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31

Ron, Eyal [Verfasser]. "Hysteresis-Delay Differential Equations / Eyal Ron." Berlin : Freie Universität Berlin, 2016. http://d-nb.info/1121588026/34.

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32

Zhang, Qi. "Stationary solutions of stochastic partial differential equations and infinite horizon backward doubly stochastic differential equations." Thesis, Loughborough University, 2008. https://dspace.lboro.ac.uk/2134/34040.

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In this thesis we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between solutions of backward doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary solutions of the SPDEs. For this, we prove the existence and uniqueness of the L2ρ (Rd; R1) × L2ρ (Rd; Rd) valued solutions of BDSDEs with Lipschitz nonlinear term on both finite and infinite horizons, so obtain the solutions of initial value problems and the stationary weak solutions (independent of any initial value) of SPDEs. Also the L2

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33

Zhang, Wenkui. "Numerical analysis of delay differential and integro-differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0011/NQ42489.pdf.

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34

Mu, Tingshu. "Backward stochastic differential equations and applications : optimal switching, stochastic games, partial differential equations and mean-field." Thesis, Le Mans, 2020. http://www.theses.fr/2020LEMA1023.

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Cette thèse est relative aux Equations Différentielles Stochastique Rétrogrades (EDSRs) réfléchies avec deux obstacles et leurs applications aux jeux de switching de somme nulle, aux systèmes d’équations aux dérivées partielles, aux problèmes de mean-field. Il y a deux parties dans cette thèse. La première partie porte sur le switching optimal stochastique et est composée de deux travaux. Dans le premier travail, nous montrons l’existence de la solution d’un système d’EDSR réfléchies à obstacles bilatéraux interconnectés dans le cadre probabiliste général. Ce problème est lié à un jeu de switc

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35

Hines, Gwendolen. "Dependence of the attractor on the delay for delay-differential equations." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/28954.

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36

Rassias, Stamatiki. "Stochastic functional differential equations and applications." Thesis, University of Strathclyde, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486536.

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The general truth that the principle of causality, that is, the future state of a system is independent of its past history, cannot support all the cases under consideration, leads to the introduction of the FDEs. However, the strong need of modelling real life problems, demands the inclusion of stochasticity. Thus, the appearance of the SFDEs (special case of which is the SDDEs) is necessary and definitely unavoidable. It has been almost a century since Langevin's model that the researchers incorporate noise terms into their work. Two of the main research interests are linked with the existen

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37

Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.

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In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the s

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38

Curry, Charles. "Algebraic structures in stochastic differential equations." Thesis, Heriot-Watt University, 2014. http://hdl.handle.net/10399/2791.

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We define a new numerical integration scheme for stochastic differential equations driven by Levy processes with uniformly lower mean square remainder than that of the scheme of the same strong order of convergence obtained by truncating the stochastic Taylor series. In doing so we generalize recent results concerning stochastic differential equations driven by Wiener processes. The aforementioned works studied integration schemes obtained by applying an invertible mapping to the stochastic Taylor series, truncating the resulting series and applying the inverse of the original mapping. The shu

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39

Rajotte, Matthew. "Stochastic Differential Equations and Numerical Applications." VCU Scholars Compass, 2014. http://scholarscompass.vcu.edu/etd/3383.

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We will explore the topic of stochastic differential equations (SDEs) first by developing a foundation in probability theory and It\^o calculus. Formulas are then derived to simulate these equations analytically as well as numerically. These formulas are then applied to a basic population model as well as a logistic model and the various methods are compared. Finally, we will study a model for low dose anthrax exposure which currently implements a stochastic probabilistic uptake in a deterministic differential equation, and analyze how replacing the probablistic uptake with an SDE alters the d

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40

Ballinger, George Henri. "Qualitative theory of impulsive delay differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ51178.pdf.

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41

Wille, David Richard. "The numerical solution of delay-differential equations." Thesis, University of Manchester, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.291519.

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42

Lumb, Patricia M. "Delay differential equations : detection of small solutions." Thesis, University of Chester, 2004. http://hdl.handle.net/10034/68595.

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This thesis concerns the development of a method for the detection of small solutions to delay differential equations. The detection of small solutions is important because their presence has significant influence on the analytical prop¬erties of an equation. However, to date, analytical methods are of only limited practical use. Therefore this thesis focuses on the development of a reliable new method, based on finite order approximations of the underlying infinite dimen¬sional problem, which can detect small solutions. Decisions (concerning the existence, or otherwise, of small solutions) ba

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43

Ezeofor, Victory S. "Analysis of differential-delay equations for biology." Thesis, University of Nottingham, 2017. http://eprints.nottingham.ac.uk/39940/.

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In this thesis, we investigate the role of time delay in several differential-delay equation focusing on the negative autogenous regulation. We study these models for little or no delay to when the model has a very large delay parameter. We start with the logistic differential-delay equation applying techniques that would be used in subsequent chapters for other models being studied. A key goal of this research is to identify where the structure of the system does change. First, we investigate these models for critical point and study their behaviour close to these points. Of keen interest is

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44

Gallage, Roshini Samanthi. "Approximation Of Continuously Distributed Delay Differential Equations." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/theses/2196.

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We establish a theorem on the approximation of the solutions of delay differential equations with continuously distributed delay with solutions of delay differential equations with discrete delays. We present numerical simulations of the trajectories of discrete delay differential equations and the dependence of their behavior for various delay amounts. We further simulate continuously distributed delays by considering discrete approximation of the continuous distribution.

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45

Zhou, Ziqian. "Statistical inference of distributed delay differential equations." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2173.

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In this study, we aim to develop new likelihood based method for estimating parameters of ordinary differential equations (ODEs) / delay differential equations (DDEs) models. Those models are important for modeling dynamical processes that are described in terms of their derivatives and are widely used in many fields of modern science, such as physics, chemistry, biology and social sciences. We use our new approach to study a distributed delay differential equation model, the statistical inference of which has

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46

Nie, Tianyang. "Stochastic differential equations with constraints on the state : backward stochastic differential equations, variational inequalities and fractional viability." Thesis, Brest, 2012. http://www.theses.fr/2012BRES0047.

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Le travail de thèse est composé de trois thèmes principaux : le premier étudie l'existence et l'unicité pour des équations différentielles stochastiques (EDS) progressives-rétrogrades fortement couplées avec des opérateurs sous-différentiels dans les deux équations, dans l’équation progressive ainsi que l’équation rétrograde, et il discute également un nouveau type des inégalités variationnelles partielles paraboliques associées, avec deux opérateurs sous-différentiels, l’un agissant sur le domaine de l’état, l’autre sur le co-domaine. Le second thème est celui des EDS rétrogrades sans ainsi q

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47

Yalman, Hatice. "Change Point Estimation for Stochastic Differential Equations." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5748.

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<p>A stochastic differential equationdriven by a Brownian motion where the dispersion is determined by a parameter is considered. The parameter undergoes a change at a certain time point. Estimates of the time change point and the parameter, before and after that time, is considered.The estimates were presented in Lacus 2008. Two cases are considered: (1) the drift is known, (2) the drift is unknown and the dispersion space-independent. Applications to Dow-Jones index 1971-1974 and Goldmann-Sachs closings 2005-- May 2009 are given.</p>

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48

Leng, Weng San. "Backward stochastic differential equations and option pricing." Thesis, University of Macau, 2003. http://umaclib3.umac.mo/record=b1447308.

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49

Tunc, Vildan. "Two Studies On Backward Stochastic Differential Equations." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614541/index.pdf.

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Backward stochastic differential equations appear in many areas of research including mathematical finance, nonlinear partial differential equations, financial economics and stochastic control. The first existence and uniqueness result for nonlinear backward stochastic differential equations was given by Pardoux and Peng (Adapted solution of a backward stochastic differential equation. System and Control Letters, 1990). They looked for an adapted pair of processes {x(t)<br>y(t)}<br>t is in [0<br>1]} with values in Rd and Rd&times<br>k respectively, which solves an equation of the form: x(t) +

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Zettervall, Niklas. "Multi-scale methods for stochastic differential equations." Thesis, Umeå universitet, Institutionen för fysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-53704.

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Standard Monte Carlo methods are used extensively to solve stochastic differential equations. This thesis investigates a Monte Carlo (MC) method called multilevel Monte Carlo that solves the equations on several grids, each with a specific number of grid points. The multilevel MC reduces the computational cost compared to standard MC. When using a fixed computational cost the variance can be reduced by using the multilevel method compared to the standard one. Discretization and statistical error calculations are also being conducted and the possibility to evaluate the errors coupled with the m

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