An averaging principle for fractional stochastic differential equations with Lévy noise

Abstract

This paper is devoted to the study of an averaging principle for fractional stochastic differential equations in Rn with Lévy motion, using an integral transform method. We obtain a time-averaged effective equation under suitable assumptions. Furthermore, we show that the solutions of the averaged equation approach the solutions of the original equation. Our results provide a better understanding for effective approximation of fractional dynamical systems with non-Gaussian Lévy noise.