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 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 goes to zero in the supremum‐ and Hölder ‐ topologies, which are sharpen existing ones in the classical McKean–Vlasov SDEs framework.