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

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 X ɛ converges to the solution X ̄ of the corresponding averaged equation in L 2 (Ω , C ([ 0 , T ] , R n)) 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. [ABSTRACT FROM AUTHOR]