Relevant bibliographies by topics / Stochastické obyčejné diferenciální rovnice / Dissertations / Theses
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Dissertations / Theses on the topic 'Stochastické obyčejné diferenciální rovnice'

Author: Grafiati
Published: 4 June 2021
Last updated: 12 February 2022

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Consult the top 24 dissertations / theses for your research on the topic 'Stochastické obyčejné diferenciální rovnice.'

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1

Bahník, Michal. "Stochastické obyčejné diferenciálni rovnice." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-232074.

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Diplomová práce se zabývá problematikou obyčejných stochastických diferenciálních rovnic. Po souhrnu teorie stochastických procesů, zejména tzv. Brownova pohybu je zaveden stochastický Itôův integrál, diferenciál a tzv. Itôova formule. Poté je definováno řešení počáteční úlohy stochastické diferenciální rovnice a uvedena věta o existenci a jednoznačnosti řešení. Pro případ lineární rovnice je odvozen tvar řešení a rovnice pro jeho střední hodnotu a rozptzyl. Závěr tvoří rozbor vybraných rovnic.
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2

Archalousová, Olga. "Singulární počáteční úloha pro obyčejné diferenciální a integrodiferenciální rovnice." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2011. http://www.nusl.cz/ntk/nusl-233525.

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The thesis deals with qualitative properties of solutions of singular initial value problems for ordinary differential and integrodifferential equations which occur in the theory of linear and nonlinear electrical circuits and the theory of therminionic currents. The research is concentrated especially on questions of existence and uniqueness of solutions, asymptotic estimates of solutions and modications of Adomian decomposition method for singular initial problems. Solution algoritms are derived for scalar differential equations of Lane-Emden type using Taylor series and modication of the Ad
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3

Janečka, Adam. "Stochastické rovnice a numerické řešení modelu oceňování opcí." Master's thesis, Vysoká škola ekonomická v Praze, 2012. http://www.nusl.cz/ntk/nusl-195450.

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In the present work, we study the topic of stochastic differential equations, their numerical solution and solution of models for pricing of options which follow from stochastic differential equations using the Itô calculus. We present several numerical methods for solving stochastic differential equations. These methods are then implemented in MATLAB and we investigate their properties, especially their convergence characteristics. Furthermore, we formulate two models for pricing of European call options. We solve these models using a variant of the spectral collocation method, again in MATLA
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Nečasová, Gabriela. "Paralelní numerické řešení parciálních diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2014. http://www.nusl.cz/ntk/nusl-236119.

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This thesis deals with the topic of partial differential equations parallel solutions. First, it focuses on ordinary differential equations (ODE) and their solution methods using Taylor polynomial. Another part is devoted to partial differential equations (PDE). There are several types of PDE, there are parabolic, hyperbolic and eliptic PDE. There is also explained how to use TKSL system for PDE computing. Another part focuses on solution methods of PDE, these methods are forward, backward and combined methods. There was explained, how to solve these methods in TKSL and Matlab systems. Computi
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Šátek, Václav. "Analýza stiff soustav diferenciálních rovnic." Doctoral thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2012. http://www.nusl.cz/ntk/nusl-261258.

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The solving of stiff systems is still a contemporary sophisticated problem. The basic problem is the absence of precise definition of stiff systems. A question is also how to detect the stiffness in a given system of differential equations. Implicit numerical methods are commonly used for solving stiff systems. The stability domains of these methods are relatively large but the order of them is low.   The thesis deals with numerical solution of ordinary differential equations, especially numerical calculations using Taylor series methods. The source of stiffness is analyzed and the possibility
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Kluknavský, František. "Vliv přesnosti aritmetických operací na přesnost numerických metod." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2012. http://www.nusl.cz/ntk/nusl-236465.

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Thesis is dedicated to evaluation of roundoff impact on numerical integration methods accuracy and effectivity. Contains theoretical expectations taken from existing literature, implementation of chosen methods, experimental measurement of attained accuracy under different circumstances and their comparison with regard to time complexity. Library contains Runge-Kutta methods to order 7 and Adams-Bashforth methods to order 20 implemented using C++ templates which allow optional arbitrary-precision arithmetic. Small models with known analytic solution were used for experiments.
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7

Kopřiva, Jan. "Semi - analytické výpočty a spojitá simulace." Doctoral thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2014. http://www.nusl.cz/ntk/nusl-261241.

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The thesis deals with speedup and accuracy of numerical computation, especially when differential equations are solved. Algorithms, which are fulling these conditions are named semi-analytical. One posibility how to accelerate computation of differential equation is paralelization. Presented paralelization is based on transformation numerical solution into residue number system, which is extended to floating point computation. A new algorithm for modulo multiplication is also proposed. As application applications in solution of differential calculus are the main goal it is discussed numeric in
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8

Sehnalová, Pavla. "Stabilita a konvergence numerických výpočtů." Doctoral thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2011. http://www.nusl.cz/ntk/nusl-261248.

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Tato disertační práce se zabývá analýzou stability a konvergence klasických numerických metod pro řešení obyčejných diferenciálních rovnic. Jsou představeny klasické jednokrokové metody, jako je Eulerova metoda, Runge-Kuttovy metody a nepříliš známá, ale rychlá a přesná metoda Taylorovy řady. V práci uvažujeme zobecnění jednokrokových metod do vícekrokových metod, jako jsou Adamsovy metody, a jejich implementaci ve dvojicích prediktor-korektor. Dále uvádíme generalizaci do vícekrokových metod vyšších derivací, jako jsou např. Obreshkovovy metody. Dvojice prediktor-korektor jsou často implement
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9

Kocina, Filip. "Moderní metody modelování a simulace elektronických obvodů." Doctoral thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2017. http://www.nusl.cz/ntk/nusl-412585.

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Disertační práce se zabývá simulací elektronických obvodů. Popisuje metodu kapacitorové substituce (CSM) pro převod elektronických obvodů na elektrické obvody, jež mohou být následně řešeny pomocí numerických metod, zejména Moderní metodou Taylorovy řady (MTSM). Tato metoda se odlišuje automatickým výběrem řádu, půlením kroku v případě potřeby a rozsáhlou oblastí stability podle zvoleného řádu. V rámci disertační práce bylo autorem disertace vytvořeno specializované programové vybavení pro řešení obyčejných diferenciálních rovnic pomocí MTSM, s mnoha vylepšeními v algoritmech (v porovnání s TK
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10

Drašnar, Jan. "Stochastické modely epidemií." Master's thesis, 2016. http://www.nusl.cz/ntk/nusl-346767.

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This thesis uses a simple deterministic model represented by an ordinary di- fferential equation with two equilibrium points - depending on the initial state the illness either vanishes or persists forever. This model is expanded by adding some diffusion coefficients leading to different stochastic differential equations. They are analyzed to show how the choice of diffusion coefficients changes be- havior of the model in proximity of its equilibria and near the boundary of area with biological meaning. The theoretical results are than illustrated by computer simulations. 1
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11

NOVÁKOVÁ, Soňa. "Obyčejné diferenciální rovnice a jejich aplikace." Master's thesis, 2006. http://www.nusl.cz/ntk/nusl-43153.

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12

Skovajsa, Břetislav. "Zobecněné obyčejné diferenciální rovnice v metrických prostorech." Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-340897.

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The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.
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13

Janák, Josef. "Stochastické diferenciální rovnice s Gaussovským šumem." Doctoral thesis, 2018. http://www.nusl.cz/ntk/nusl-389647.

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Title: Stochastic Differential Equations with Gaussian Noise Author: Josef Janák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Bohdan Maslowski, DrSc., Department of Probability and Mathematical Statistics Abstract: Stochastic partial differential equations of second order with two un- known parameters are studied. The strongly continuous semigroup (S(t), t ≥ 0) for the hyperbolic system driven by Brownian motion is found as well as the formula for the covariance operator of the invariant measure Q (a,b) ∞ . Based on ergodicity, two suitable families
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14

Hofmanová, Martina. "Degenerované parabolické stochastické parciální diferenciální rovnice." Doctoral thesis, 2013. http://www.nusl.cz/ntk/nusl-322207.

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In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyper- bolic 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
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15

Lavička, Karel. "Invariantní míry pro dissipativní stochastické diferenciální rovnice." Master's thesis, 2012. http://www.nusl.cz/ntk/nusl-305072.

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The main topic of this Thesis is a new simplified proof of the Sunyach theorem that provides suffici- ent conditions for existence and uniqueness of an invariant measure for a Markov kernel on a complete separable metric space equipped with its Borel σ-algebra. Weak convergence of measures following from Sunyach's theorem is strengthened to convergence in the total variation norm provided that the Markov kernel is strong Feller. Furthermore, sufficient conditions for geometric ergodicity are stated. Another topic treated is the strong Feller property: its characterization by absolute measurabi
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16

Camfrlová, Monika. "Stochastické diferenciální rovnice s gaussovským šumem a jejich aplikace." Master's thesis, 2020. http://www.nusl.cz/ntk/nusl-434536.

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In the thesis, multivariate fractional Brownian motions with possibly different Hurst indices in different coordinates are considered and a Girsanov-type theo- rem for these processes is shown. Two applications of this theorem to stochastic differential equations driven by multivariate fractional Brownian motions (SDEs) are given. Firstly, the existence of a weak solution to an SDE with a drift coeffi- cient that can be written as a sum of a regular and a singular part and a diffusion coefficient that is dependent on time and satisfies suitable conditions is shown. The results are applied for
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17

Zahradník, Petr. "Jednorozměrné difusní stochastické diferenciální rovnice s aplikacemi ve finanční matematice." Master's thesis, 2010. http://www.nusl.cz/ntk/nusl-299000.

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In this thesis, the aim is to employ some of the advanced probability and calculus techniques to financial mathematics. In the first chapter some major facts from continuous - time probability theory are presented. In the second chapter, one - dimensional stochastic diferential equations are introduced, we touch upon the questions of existence and uniqueness of solutions in full generality, construct a weak solution to the Engelbert - Schmidt equation and thoroughly present a known procedure called a Feller's test for explosions. In chapter three, focus is directed to a brief presentation of t
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18

Kršek, Daniel. "Semilineární stochastické evoluční rovnice." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448080.

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Stochastic partial differential equations have proven useful in many applied areas of mathematics, such as physics or mathematical finance. A major part of such equations consists of linear equations with additive noise. In certain cases, however, the drift part of the differential equation additionally contains a possibly problematic non-linear term, which makes it unsolvable by the standard methods and even a solution in the mild sense may be out of reach. In such situations, we may still find a solution in the weak sense by employing a suitable transformation of the probability space. This
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19

Šnupárková, Jana. "Stochastické evoluční rovnice s multiaplikativním frakcionálním šumem." Doctoral thesis, 2012. http://www.nusl.cz/ntk/nusl-305906.

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Title: Stochastic evolution equations with multiplicative fractional noise Author: Jana Šnupárková Departement: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Bohdan Maslowski, DrSc. Supervisor's e-mail address: maslow@karlin.mff.cuni.cz Abstract: The fractional Gaussian noise is a formal derivative of a fractional Brownian motion with Hurst parameter H ∈ (0, 1). An explicit formula for a solution to stochastic differential equations with a multiplicative fractional Gaussian noise in a separable Hilbert space is given. The large time behaviour of the solution is
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20

Žák, František. "Markovské semigrupy." Master's thesis, 2012. http://www.nusl.cz/ntk/nusl-305470.

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In the presented work we study the existence of periodic solution to infinite dimensional stochastic equation with periodic coefficients driven by Cylindrical Wiener process. Used theory of infinite dimensional stochastic equations in Hilbert spaces and Markov processes is summarized in the first two chapters. In the third and last chapter we present the result itself. Necessary technical background mostly from operator theory is encapsulated in the Appendix. The proof of existence of periodic solution of corresponding equation is a combination of arguments by Khasminskii, which ensure under s
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Čoupek, Petr. "Stochastické integrály řízené isonormálními gaussovskými procesy a aplikace." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-328307.

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Stochastic Integrals Driven by Isonormal Gaussian Processes and Applications Master Thesis - Petr Čoupek Abstract In this thesis, we introduce a stochastic integral of deterministic Hilbert space valued functions driven by a Gaussian process of the Volterra form βt = t 0 K(t, s)dWs, where W is a Brownian motion and K is a square integrable kernel. Such processes generalize the fractional Brownian motion BH of Hurst parameter H ∈ (0, 1). Two sets of conditions on the kernel K are introduced, the singular case and the regular case, and, in particular, the regular case is studied. The main result
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22

Vostal, Ondřej. "Lineárně kvadratické optimální řízení ve spojitém čase." Master's thesis, 2017. http://www.nusl.cz/ntk/nusl-367653.

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We partially solve the adaptive ergodic stochastic optimal control problem where the driving process is a fractional Brownian motion with Hurst parameter H > 1/2. A formula is provided for an optimal feedback control given a strongly consistent estimator of the parameters of the controlled system is avail- able. There are some special conditions imposed on the estimator which means the results are not completely general. They apply, for example, in the case where the estimator is independent of the driving fractional Brownian motion. In the course of the thesis, construction of stochastic inte
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Pacák, Daniel. "Odhad parametru ve stochastických diferenciálních rovnicích." Master's thesis, 2020. http://www.nusl.cz/ntk/nusl-434533.

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In the Thesis the problem of estimating an unknown parameter in a stochastic dif- ferential equation is studied. Linear equations with Volterra process as the source of noise are considered. Firstly, the properties of Volterra processes and the properties of stochastic integral with respect to a Volterra process are presented. Secondly, the prop- erties of the solution to the equation under consideration are discussed. This includes the existence of the strictly stationary solution, the properties of such solution and ergodic results. These results are then generalized to equations with a mixe
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Týbl, Ondřej. "Kalmanův-Bucyho filtr ve spojitém čase." Master's thesis, 2019. http://www.nusl.cz/ntk/nusl-397771.

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In the Thesis we study the problem of linear filtration of Gaussian signals in finite-dimensional space. We use the Kalman-type equations for the filter to show that the filter depends continuously on the signal. Secondly, we show the same continuity property for the covariance of the error and verify existence and uniqueness of a solution to an integral equation that is satisfied by the filter even under more general assumptions. We present several examples of application of the continuity property that are based on the theory of stochastic differential equations driven by fractional Brownian
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