Second-Order McKean-Vlasov Stochastic Evolution Equation Driven by Poisson Jumps: Existence, Uniqueness and Averaging Principle

In this paper, a class of second-order McKean–Vlasov stochastic evolution equations driven by Poisson jumps with non-Lipschitz conditions is considered. The existence and uniqueness of the mild solution are established by means of the Carathéodory approximation technique. Furthermore, an averaging principle is obtained between the solution of the second-order McKean–Vlasov stochastic evolution equation and that of the simplified equation in the mean-square sense.