Strong convergence rate for slow-fast stochastic differential equations with Markovian switching

Abstract

In this paper, we study the averaging principle for a class of slow-fast stochastic differential equations with Markovian switching, where the slow component is the solution of a stochastic differential equation and the fast component is a Markov chain. Using the technique of Poisson equation and mollifying approximation, the optimal strong convergence order $ 1/2 $ is obtained under the Lipschitz continuous condition.