Averaging principle for stochastic differential equations with monotone condition

Zhongkai Guo, Yong Xu, Weifeng Wang, Junhao Hu

Abstract: In this paper, we consider the averaging principle for a class of stochastic differential equations (SDEs) with the nonlinear terms only satisfying the local Lipschitz and monotone conditions. Compared with the classical Lipschitz and linear growth conditions, conditions given in this paper are relatively weak, so the conclusions obtained in this paper are suitable for a wider class of SDEs.