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BAŠTINEC, J. KLIMEŠOVÁ, M.
Originální název
Stability of the Zero Solution of Stochastic Differential Systems with Two-dimensional Brownian motion
Typ
článek ve sborníku ve WoS nebo Scopus
Jazyk
angličtina
Originální abstrakt
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 the asymptotic 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.
Klíčová slova
Brownian motion, stochastic differential equation, Lyapunov function, stochastic Lyapunov function, stability, stochastic stability.
Autoři
BAŠTINEC, J.; KLIMEŠOVÁ, M.
Vydáno
5. 1. 2016
Nakladatel
UNOB
Místo
Brno
ISBN
978-80-7231-436-2
Kniha
Mathematics, Information Technologiies, and Applied Science 2015
Číslo edice
1
Strany od
8
Strany do
20
Strany počet
13
BibTex
@inproceedings{BUT121476, author="Jaromír {Baštinec} and Marie {Klimešová}", title="Stability of the Zero Solution of Stochastic Differential Systems with Two-dimensional Brownian motion", booktitle="Mathematics, Information Technologiies, and Applied Science 2015", year="2016", number="1", pages="8--20", publisher="UNOB", address="Brno", isbn="978-80-7231-436-2" }