A Stochastic Analog of Bogolyubov’s Second Theorem - Bondarev, B. V.; Kovtun, E. E. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
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.