Publication detail

Stability of the Zero Solution of Stochastic Differential Systems with Two-dimensional Brownian motion

BAŠTINEC, J. KLIMEŠOVÁ, M.

Original Title

Stability of the Zero Solution of Stochastic Differential Systems with Two-dimensional Brownian motion

English Title

Stability of the Zero Solution of Stochastic Differential Systems with Two-dimensional Brownian motion

Type

conference paper

Language

en

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.

English 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.

Released

05.01.2016

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

Documents

BibTex


@inproceedings{BUT121476,
  author="Jaromír {Baštinec} and Marie {Klimešová}",
  title="Stability of the Zero Solution of Stochastic Differential
Systems with Two-dimensional Brownian motion",
  annote="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.",
  address="UNOB",
  booktitle="Mathematics, Information Technologiies, and Applied Science 2015",
  chapter="121476",
  howpublished="electronic, physical medium",
  institution="UNOB",
  year="2016",
  month="january",
  pages="8--20",
  publisher="UNOB",
  type="conference paper"
}