Detail publikačního výsledku

Stability of Stochastic Differential Systems

KLIMEŠOVÁ, M.; BAŠTINEC, J.

Originální název

Stability of Stochastic Differential Systems

Anglický název

Stability of Stochastic Differential Systems

Druh

Stať ve sborníku v databázi WoS či Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

KLIMEŠOVÁ, M.; BAŠTINEC, J.

Rok RIV

2016

Vydáno

18.06.2015

Nakladatel

Univerzita obrany

Místo

Brno

ISBN

978-80-7231-998-5

Kniha

Matematika, informační technologie a aplikované vědy (MITAV 2015)

ISSN

NEUVEDENO

Strany od

1

Strany do

9

Strany počet

9

BibTex

@inproceedings{BUT114984,
  author="Marie {Klimešová} and Jaromír {Baštinec}",
  title="Stability of Stochastic Differential Systems",
  booktitle="Matematika, informační technologie a aplikované vědy (MITAV 2015)",
  year="2015",
  number="1",
  pages="1--9",
  publisher="Univerzita obrany",
  address="Brno",
  isbn="978-80-7231-998-5"
}