Publication detail

Stability of Stochastic Differential Systems

KLIMEŠOVÁ, M. BAŠTINEC, J.

Original Title

Stability of Stochastic Differential Systems

English Title

Stability of Stochastic Differential Systems

Type

conference paper

Language

en

Original Abstract

This paper surveys the elementary theory of stability of solution of stochastic differential equations (SDEs) and systems. It can be used in population models, epidemic and genetic models in medicine and biology, meteorology models, in physical science, for analysis in economy, financial mathematics, etc. The article starts with a review of the stochastic theory. Then, conditions are deduced 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. It is used a Lyapunov function. The method of Lyapunov functions for the analysis of 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.

English abstract

This paper surveys the elementary theory of stability of solution of stochastic differential equations (SDEs) and systems. It can be used in population models, epidemic and genetic models in medicine and biology, meteorology models, in physical science, for analysis in economy, financial mathematics, etc. The article starts with a review of the stochastic theory. Then, conditions are deduced 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. It is used a Lyapunov function. The method of Lyapunov functions for the analysis of 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.

Keywords

Brownian motion, stochastic differential equation, Lyapunov function, stochastic Lyapunov function, stability, stochastic stability

RIV year

2015

Released

18.06.2015

Publisher

Univerzita obrany

Location

Brno

ISBN

978-80-7231-998-5

Book

Matematika, informační technologie a aplikované vědy (MITAV 2015)

Edition number

1

Pages from

1

Pages to

9

Pages count

9

Documents

BibTex


@inproceedings{BUT114984,
  author="Marie {Klimešová} and Jaromír {Baštinec}",
  title="Stability of Stochastic Differential Systems",
  annote="This paper surveys the elementary theory of stability of solution of stochastic differential equations (SDEs) and systems. It can be used in population models, epidemic and genetic models in medicine and biology, meteorology models, in physical science, for analysis in economy, financial mathematics, etc. The
article starts with a review of the stochastic theory. Then, conditions are deduced 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. It is used a Lyapunov function. The method of Lyapunov functions
for the analysis of 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.",
  address="Univerzita obrany",
  booktitle="Matematika, informační technologie a aplikované vědy (MITAV 2015)",
  chapter="114984",
  howpublished="electronic, physical medium",
  institution="Univerzita obrany",
  year="2015",
  month="june",
  pages="1--9",
  publisher="Univerzita obrany",
  type="conference paper"
}