Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 139, Pages 91–103 (Mi into227)  
Stochastic perturbations of stable dynamical systems: trajectory-wise approach

O. A. Sultanovab

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
b Peoples Friendship University of Russia, Moscow
Full-text PDF (203 kB)
Abstract: We study stochastic perturbations of a dynamical system with a locally stable fixed point. The perturbed system has the form of Ito stochastic differential equations. We assume that perturbations do not vanish at the equilibrium of the deterministic system. Using the trajectory-wise approach to the analysis of stochastic differential equations, we find restrictions for perturbations under which the stability of the equilibrium is preserved with probability 1.
Keywords: dynamical system, perturbation, white noise, stochastic differential equation, stability with probability 1.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.a03.21.0008
This work was partially supported by the Ministry of Education and Science of the Russian Federation (project No. 02.a03.21.0008).
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 3, Pages 340–353
DOI: https://doi.org/10.1007/s10958-019-04428-1
Bibliographic databases:
Document Type: Article
UDC: 517.925.51
MSC: 93E15, 34D10, 60H10
Language: Russian
Citation: O. A. Sultanov, “Stochastic perturbations of stable dynamical systems: trajectory-wise approach”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 139, VINITI, M., 2017, 91–103; Journal of Mathematical Sciences, 241:3 (2019), 340–353
Citation in format AMSBIB
\Bibitem{Sul17}
\by O.~A.~Sultanov
\paper Stochastic perturbations of stable dynamical systems: trajectory-wise approach
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 139
\pages 91--103
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into227}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3799909}
\zmath{https://zbmath.org/?q=an:1428.93122}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 3
\pages 340--353
\crossref{https://doi.org/10.1007/s10958-019-04428-1}
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