Stability of the Zero Solution of Stochastic Differential Systems with Four-Dimensional Brownian Motion

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F16%3APU121848" target="_blank" >RIV/00216305:26220/16:PU121848 - isvavai.cz</a>

Výsledek na webu

<a href="http://mitav.unob.cz/data/MITAV%202016%20Proceedings.pdf" target="_blank" >http://mitav.unob.cz/data/MITAV%202016%20Proceedings.pdf</a>

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

Stability of the Zero Solution of Stochastic Differential Systems with Four-Dimensional Brownian Motion

Popis výsledku v původním jazyce

The natural world is influenced by stochasticity therefore stochastic models are used to test various situations because only the stochastic model can approximate the real model. For example, the stochastic model is used in population, epidemic and genetic simulations in medicine and biology, for simulations in physical and technical sciences, for analysis in economy, financial mathematics, etc. The crucial characteristic of the stochastic model is its stability. Stability of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its applications. This article studies the fundamental theory of the stochastic stability. There is investigated the stability of the solution of stochastic differential equations and systems of SDEs. The article begins with a summary of the stochastic theory. Then, there are inferred conditions for the asymptotic mean square stability of the zero solution of stochastic system with Brownian motion. There is used a Lyapunov function for proofs of main results. The method of Lyapunov functions for the analysis of qualitative behavior of SDEs provides some very useful information in the study of stability properties for concrete stochastic dynamical systems, conditions of existence the stationary solutions of SDEs and related problems. There are proved conditions for the stability (asymptotic, stochastic asymptotic). The results are illustrated by trivial examples for special types of matrices.

Název v anglickém jazyce

Stability of the Zero Solution of Stochastic Differential Systems with Four-Dimensional Brownian Motion

Popis výsledku anglicky

The natural world is influenced by stochasticity therefore stochastic models are used to test various situations because only the stochastic model can approximate the real model. For example, the stochastic model is used in population, epidemic and genetic simulations in medicine and biology, for simulations in physical and technical sciences, for analysis in economy, financial mathematics, etc. The crucial characteristic of the stochastic model is its stability. Stability of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its applications. This article studies the fundamental theory of the stochastic stability. There is investigated the stability of the solution of stochastic differential equations and systems of SDEs. The article begins with a summary of the stochastic theory. Then, there are inferred conditions for the asymptotic mean square stability of the zero solution of stochastic system with Brownian motion. There is used a Lyapunov function for proofs of main results. The method of Lyapunov functions for the analysis of qualitative behavior of SDEs provides some very useful information in the study of stability properties for concrete stochastic dynamical systems, conditions of existence the stationary solutions of SDEs and related problems. There are proved conditions for the stability (asymptotic, stochastic asymptotic). The results are illustrated by trivial examples for special types of matrices.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Mathematics, Information Technologies and Applied Sciences 2016 (post-conference proceedings of extended versions of selected papers )

ISBN

978-80-7231-400-3

ISSN

—

e-ISSN

—

Počet stran výsledku

111

Strana od-do

7-30

Název nakladatele

University of Defence

Místo vydání

Brno

Místo konání akce

Brno

Datum konání akce

16. 6. 2016

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000391451200001