Stability of the Zero Solution of Stochastic Differential Systems with Two-dimensional Brownian motion

Kód výsledku v IS VaVaI

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Nalezeny alternativní kódy

RIV/00216305:26220/16:PU117762

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Stability of the Zero Solution of Stochastic Differential Systems with Two-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. This article studies the fundamental theory of the stochastic stability. There is investigated the stability of the solution of stochastic differential equations (SDEs) and systems of SDEs. The article begins with a summary of the stochastic theory. Then, there are inferred conditions for theasymptotic mean square stability of the zero solution of stochastic equation with one-dimensional Brownian motion and system with two-dimensional Brownian motion. There is used a Lyapunov function for proofs of main results.

Název v anglickém jazyce

Stability of the Zero Solution of Stochastic Differential Systems with Two-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. This article studies the fundamental theory of the stochastic stability. There is investigated the stability of the solution of stochastic differential equations (SDEs) and systems of SDEs. The article begins with a summary of the stochastic theory. Then, there are inferred conditions for theasymptotic mean square stability of the zero solution of stochastic equation with one-dimensional Brownian motion and system with two-dimensional Brownian motion. There is used a Lyapunov function for proofs of main results.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

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 2015

ISBN

978-80-7231-436-2

ISSN

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e-ISSN

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Počet stran výsledku

14

Strana od-do

8-20

Název nakladatele

University of Defence

Místo vydání

Brno

Místo konání akce

Univerzita Obrany, Brno

Datum konání akce

18. 6. 2015

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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