2018
Том 70
№ 5

# A Stochastic Analog of Bogolyubov's Second Theorem

Abstract

We establish an estimate for the rate at which a solution of an ordinary differential equation subject to the action of an ergodic random process converges to a stationary solution of a deterministic averaged system on time intervals of order $e^{1/ερ}$ for some $0 < ρ < 1$.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 7, pp 1035-1054.

Citation Example: Bondarev B. V., Kovtun E. E. A Stochastic Analog of Bogolyubov's Second Theorem // Ukr. Mat. Zh. - 2005. - 57, № 7. - pp. 879–894.

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