Strong averaging principle for two-time-scale SDEs with non-Lipschitz coefficients

Abstract

This paper deals with averaging principle for two-time-scale stochastic differential equations (SDEs) with non-Lipschitz coefficients, which extends the existing results: from Lipschitz to non-Lipschitz case. Under suitable conditions, the existence of an averaging equation eliminating the fast variable for coupled system is established, and as a result, the system can be reduced to a single SDEs with a modified coefficient which is also non-Lipschitz. Moreover, it is shown that the slow variable strongly converges to the solution of the corresponding averaging equation.