Strong and weak convergence rates for slow–fast stochastic differential equations driven by α-stable process

Abstract

In this paper, we study the averaging principle for a class of stochastic differential equations driven by α-stable processes with slow and fast time-scales, where α∈(1,2). We prove that the strong and weak convergence order are 1−1/α and 1 respectively. We show, by a simple example, that 1−1/α is the optimal strong convergence rate.