Stochastic fractional integrodifferential equations with jumps: application to an averaging principle

Abstract

In this work we deal with a stochastic fractional integrodifferential equation associated to a Poisson random measure. We first prove existence and uniqueness of solution in the case of Lipschitz coefficients but also in the non Lipschitz case. In the second part, we establish an averaging principle in the sense of Khasminskii approach for a class of this equation with non lipschitz coefficients and weak averaging conditions.