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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

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}