Optimal strong convergence rate for a class of McKean–Vlasov SDEs with fast oscillating perturbation

Abstract

In this paper, we consider the averaging principle for a class of McKean–Vlasov stochastic differential equations perturbed by a fast oscillating term. By using the technique of Poisson equation, we prove the occurrence of the averaging principle, i.e., the solution Xɛ converges to the solution X̄ of the corresponding averaged equation in L2(Ω,C([0,T],Rn)) with the optimal convergence order 1/2. To the best of authors’ knowledge, this is the first result about the strong averaging principle when the coefficients in the slow equation depends on the law of the fast component.