Title
Aproksimacije rešenja stohastičkih diferencijalnih jednačina primenom Taylor-ovih redova
Creator
Đorđević, Dušan D., 1991-
CONOR:
80075529
Copyright date
2021
Object Links
Select license
Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
License description
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Language
Serbian
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 17.12.2021.
Other responsibilities
predsednik komisije
Pilipović, Stevan
član komisije
Milošević, Marija
član komisije
Krstić, Marija
Academic Expertise
Prirodno-matematičke nauke
Academic Title
-
University
Univerzitet u Nišu
Faculty
Prirodno-matematički fakultet
Group
Odsek za matematiku i informatiku
Alternative title
The Approximations of solutions to stochastic differential equations by applying Taylor series
Publisher
[D. D. Đorđević]
Format
V, 116 str.
description
Bibliografija: str. 111-116;
Biobibliografski podaci: str. [117-118].
description
Stochastic analysis
Abstract (en)
The subject of the doctoral dissertation is the application of the Taylor formula for the coefficients of various types of stochastic differential equations, for the purpose of the approximation of theirs solutions under non standard conditions, such as the global Lipschitz condition and the linear growth condition. Under certain assumptions, the almost sure convergence and the convergence in the p-th mean, p>0, of the sequence of approximate solutions towards the solution of the initial equation, is shown. The rate of the Lp convergence increases as the orders of the Taylor approximations of the coefficients of the initial equation increase. Shown results are illustrated through the examples which are designed such that the global Lipschitz condition and/or the linear growth condition for the drift and diffusion coefficients are not satisfied. That way, the need for the shown results is satisfied. Techniques used in the proofs are determined by the type of the considered equation, as well as by the conditions which are assumed for the coefficients of the equations.
Authors Key words
Lp konvergencija, polinomijalni uslov, skoro izvesna konvergencija, stohastičke diferencijalne jednačine, stohastičke diferencijalne jednačine sa vremenski zavisnim kašnjenjem, funkcionalne stohastičke diferencijalne jednačine, neutralne stohastičke diferencijalne jednačine sa vremenskim kašnjenjem, Tejlorova aproksimacija, Frešeov izvod
Authors Key words
Lp convergence, polynomial condition, almost sure convergence, stochastic differential equations, stochastic differential equations with time dependent delay, stochastic functional differential equations, neutral stochastic differential equations with time related delay, Taylor approximation, Frechet derivative
Classification
519.216:517.9(043.3)
Subject
P130
Type
Tekst
Abstract (en)
The subject of the doctoral dissertation is the application of the Taylor formula for the coefficients of various types of stochastic differential equations, for the purpose of the approximation of theirs solutions under non standard conditions, such as the global Lipschitz condition and the linear growth condition. Under certain assumptions, the almost sure convergence and the convergence in the p-th mean, p>0, of the sequence of approximate solutions towards the solution of the initial equation, is shown. The rate of the Lp convergence increases as the orders of the Taylor approximations of the coefficients of the initial equation increase. Shown results are illustrated through the examples which are designed such that the global Lipschitz condition and/or the linear growth condition for the drift and diffusion coefficients are not satisfied. That way, the need for the shown results is satisfied. Techniques used in the proofs are determined by the type of the considered equation, as well as by the conditions which are assumed for the coefficients of the equations.
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