Averaging for systems of stochastic equations with random disturbances (Q2777843)

The author considers systems of stochastic equations with a small parameter \(\varepsilon\). The first equations have unbounded drift and coefficients which depend on the small parameter \(\varepsilon\). The second equations are described by Markov diffusion processes with periodic coefficients. Weak convergence of probability measures induced by the first equations to a certain random process is investigated. In the second part of the proof of the main theorem the technique proposed by \textit{S. Ya. Makhno} [Theory Probab. Appl. 44, No. 3, 495-510 (1999); translation from Teor. Veroyatn. Primen. 44, No. 3, 555-572 (1999; Zbl 0969.60062)] is used extensively.