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 $\mathit{\alpha }\in (1,2)$. We prove that the strong and weak convergence order are $1-1/\mathit{\alpha }$ and 1 respectively. We show, by a simple example, that $1-1/\mathit{\alpha }$ is the optimal strong convergence rate.