This paper is devoted to obtaining an averaging principle for systems of slow-fast stochastic differential equations, where the fast variable drift is periodically modulated on a fast time-scale. The approach developed here combines probabilistic methods with a recent analytical result on long-time behavior for second order elliptic equations with time-periodic coefficients.
"Double averaging principle for periodically forced stochastic slow-fast systems." Electron. Commun. Probab. 18 1 - 12, 2013. https://doi.org/10.1214/ECP.v18-1975