Publication 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

journal article in Web of Science

Language

en

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

RIV year

2015

Released

07.05.2015

Publisher

SpringerOpen

Pages count

10

URL

Full text in the Digital Library

Documents

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",
  annote="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.",
  address="SpringerOpen",
  chapter="114441",
  doi="10.1186/s13662-015-0482-y",
  howpublished="online",
  institution="SpringerOpen",
  number="143",
  volume="2015",
  year="2015",
  month="may",
  pages="0--0",
  publisher="SpringerOpen",
  type="journal article in Web of Science"
}