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Stability of equilibrium with respect to white noise

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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. Stability with given bounds is proved on a large time interval with length of the order of the squared inverse perturbation amplitude. The proof is based on the construction of a barrier function for the parabolic Kolmogorov equation associated with the perturbed dynamical system.

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Authors and Affiliations

  1. Institute of Mathematics with Computing Center, Ufa Research Center of the Russian Academy of Sciences, Ufa, 450008, Russia

    L. A. Kalyakin

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  1. L. A. Kalyakin
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Correspondence to L. A. Kalyakin.

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Original Russian Text © L.A. Kalyakin, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 21, No. 1.

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Kalyakin, L.A. Stability of equilibrium with respect to white noise. Proc. Steklov Inst. Math. 295 (Suppl 1), 68–77 (2016). https://doi.org/10.1134/S008154381609008X

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  • DOI: https://doi.org/10.1134/S008154381609008X

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