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KLIMEŠOVÁ, M. BAŠTINEC, J.
Original Title
Stability of Stochastic Differential Systems
Type
conference paper
Language
English
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.
Keywords
Brownian motion, stochastic differential equation, Lyapunov function, stochastic Lyapunov function, stability, stochastic stability
Authors
KLIMEŠOVÁ, M.; BAŠTINEC, J.
RIV year
2015
Released
18. 6. 2015
Publisher
Univerzita obrany
Location
Brno
ISBN
978-80-7231-998-5
Book
Matematika, informační technologie a aplikované vědy (MITAV 2015)
Edition number
1
NEUVEDENO
Pages from
Pages to
9
Pages count
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" }