Averaging principle for slow-fast stochastic differential equations with time dependent locally Lipschitz coefficients

Abstract

This paper is devoted to studying the averaging principle for stochastic differential equations with slow and fast time-scales, where the drift coefficients satisfy local Lipschitz conditions with respect to the slow and fast variables, and the coefficients in the slow equation depend on time $t$ and $\omega$. Making use of the techniques of time discretization and truncation, we prove that the slow component strongly converges to the solution of the corresponding averaged equation.

Page 30, this paper has been published in J. Differential Equations 268 (2020) 2910-2948