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Matematicheskie Zametki, 2017, Volume 101, Issue 1, Pages 130–139
DOI: https://doi.org/10.4213/mzm11108
(Mi mzm11108)
 

This article is cited in 4 scientific papers (total in 4 papers)

Stochastic Stability of a Dynamical System Perturbed by White Noise

O. A. Sultanov

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
Full-text PDF (485 kB) Citations (4)
References:
Abstract: The effect of small constantly acting random perturbations of white noise type on a dynamical system with locally stable fixed point is studied. The perturbed system is considered in the form of Itô stochastic differential equations, and it is assumed that the perturbation does not vanish at a fixed point. In this case, the trajectories of the stochastic system issuing from points near the stable fixed point exit from the neighborhood of equilibrium with probability $1$. Classes of perturbations such that the equilibrium of a deterministic system is stable in probability on an asymptotically large time interval are described.
Keywords: dynamical system, perturbation, white noise, stability.
Funding agency Grant number
Russian Science Foundation 14-11-00078
Received: 07.02.2016
Revised: 02.06.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 1, Pages 149–156
DOI: https://doi.org/10.1134/S0001434617010151
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: O. A. Sultanov, “Stochastic Stability of a Dynamical System Perturbed by White Noise”, Mat. Zametki, 101:1 (2017), 130–139; Math. Notes, 101:1 (2017), 149–156
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11108
  • https://www.mathnet.ru/eng/mzm/v101/i1/p130
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    References:63
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