Publication result detail

Stability of the zero solution of nonlinear differential equations under the influence of white noise

DZHALLADOVA, I.; RŮŽIČKOVÁ, M.; ŠTOUDKOVÁ RŮŽIČKOVÁ, V.

Original Title

Stability of the zero solution of nonlinear differential equations under the influence of white noise

English Title

Stability of the zero solution of nonlinear differential equations under the influence of white noise

Type

WoS Article

Original Abstract

The paper deals with a system of nonlinear differential equations under the influence of white noise. This system can be used as a mathematical model of various real problems in finance, mathematical biology, climatology, signal theory and others. Necessary and sufficient conditions for the asymptotic mean square stability of the zero solution of this system are derived in the paper. The paper introduces a new approach to studying such problems - construction of a suitable deterministic system with the use of Lyapunov function.

English abstract

The paper deals with a system of nonlinear differential equations under the influence of white noise. This system can be used as a mathematical model of various real problems in finance, mathematical biology, climatology, signal theory and others. Necessary and sufficient conditions for the asymptotic mean square stability of the zero solution of this system are derived in the paper. The paper introduces a new approach to studying such problems - construction of a suitable deterministic system with the use of Lyapunov function.

Keywords

stochastic systems; white noise; mean square stability; Lyapunov function

Key words in English

stochastic systems; white noise; mean square stability; Lyapunov function

Authors

DZHALLADOVA, I.; RŮŽIČKOVÁ, M.; ŠTOUDKOVÁ RŮŽIČKOVÁ, V.

RIV year

2016

Released

07.05.2015

Publisher

SpringerOpen

ISBN

1687-1847

Periodical

Advances in Difference Equations

Volume

2015

Number

143

State

United States of America

Pages count

10

URL

http://www.advancesindifferenceequations.com/content/2015/1/143

Full text in the Digital Library

http://hdl.handle.net/11012/137371

BibTex

@article{BUT114441,
  author="Irada {Dzhalladova} and Miroslava {Růžičková} and Viera {Štoudková Růžičková}",
  title="Stability of the zero solution of nonlinear differential equations under the influence of white noise",
  journal="Advances in Difference Equations",
  year="2015",
  volume="2015",
  number="143",
  pages="10",
  doi="10.1186/s13662-015-0482-y",
  issn="1687-1847",
  url="http://www.advancesindifferenceequations.com/content/2015/1/143"
}

Documents

s13662-015-0482-y