Strong and weak convergence rates for slow-fast stochastic differential equations driven by $\alpha$-stable process

Abstract

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

25 pages. To appear in Bernoulli