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BAŠTINEC, J. KLIMEŠOVÁ, M.
Original Title
Stability of the Zero Solution of Stochastic Differential Systems with Two-dimensional Brownian motion
Type
conference paper
Language
English
Original Abstract
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.
Keywords
Brownian motion, stochastic differential equation, Lyapunov function, stochastic Lyapunov function, stability, stochastic stability.
Authors
BAŠTINEC, J.; KLIMEŠOVÁ, M.
Released
5. 1. 2016
Publisher
UNOB
Location
Brno
ISBN
978-80-7231-436-2
Book
Mathematics, Information Technologiies, and Applied Science 2015
Edition number
1
Pages from
8
Pages to
20
Pages count
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" }