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

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 $alphain(1,2)$. 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.