A Stochastic Analog of Bogolyubov's Second Theorem

• Date: 2005
• Main Authors: Bondarev, B. V., Kovtun, E. E., Бондарев, Б. В., Ковтун, Е. Е.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3650
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $0 < ρ < 1$.