Analysis of multiscale methods for stochastic dynamical systems driven by ?-stable processes

Summary: This paper investigates the averaging principle for a class of stochastic differential equations with slow and fast time-scales driven by alpha-stable processes. It is shown that the strong and weak convergence order are 1 - 1/alpha and 1 respectively, with 1 - 1/alpha being the optimal strong convergence rate demonstrated by a simple example.