Stochastic averaging principle for McKean-Vlasov SDEs driven by Levy noise

In this paper, we study McKean-Vlasov stochastic differential equations driven by Levy processes. Firstly, under the non-Lipschitz condition which include classical Lipschitz conditions as special cases, we establish the existence and uniqueness for solutions of McKean-Vlasov stochastic differential equations using Caratheodory approximation. Then under certain averaging conditions, we establish a stochastic averaging principle for McKean-Vlasov stochastic differential equations driven by Levy processes. We find that the solutions to stochastic systems concerned with Levy noise can be approximated by solutions to averaged McKean-Vlasov stochastic differential equations driven by Levy processes in the sense of convergence in pth moment.