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Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 1, Pages 112–121 (Mi timm1147)  

Stability of equilibrium with respect to a white noise

L. A. Kalyakin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa

Abstract: A system of ordinary differential equations with a local asymptotically stable equilibrium is considered. The problem of stability with respect to a persistent perturbation of the white noise type is discussed. The stability with given estimates is proved on a large time interval with a length of the order of the squared reciprocal magnitude of the perturbation. The proof is based on the construction of a barrier function for the Kolmogorov parabolic equation associated with the perturbed dynamical system.

Keywords: dynamical system; random perturbation; stability; parabolic equation; barrier function.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, 295, suppl. 1, 68–77

Bibliographic databases:

Document Type: Article
UDC: 517.919
Received: 04.11.2014

Citation: L. A. Kalyakin, “Stability of equilibrium with respect to a white noise”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 1, 2015, 112–121; Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 68–77

Citation in format AMSBIB
\Bibitem{Kal15}
\by L.~A.~Kalyakin
\paper Stability of equilibrium with respect to a white noise
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 1
\pages 112--121
\mathnet{http://mi.mathnet.ru/timm1147}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3379608}
\elib{http://elibrary.ru/item.asp?id=23137977}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 295
\issue , suppl. 1
\pages 68--77
\crossref{https://doi.org/10.1134/S008154381609008X}


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