Averaging principle for McKean-Vlasov SDEs driven by multiplicative fractional noise with highly oscillatory drift coefficient

Abstract

In this paper, we study averaging principle for a class of McKean-Vlasov stochastic differential equations (SDEs) that contain multiplicative fractional noise with Hurst parameter $H>$ 1/2 and highly oscillatory drift coefficient. Here the integral corresponding to fractional Brownian motion is the generalized Riemann-Stieltjes integral. Using Khasminskii's time discretization techniques, we prove that the solution of the original system strongly converges to the solution of averaging system as the times scale $\hat{I}\mu$ gose to zero in the supremum- and Hölder-topologies which are sharpen existing ones in the classical Mckean-Vlasov SDEs framework.

12 pages