标题： 麦卡恩-弗拉索夫随机微分方程的平均化原理，由乘法分数噪声驱动，具有高度振荡的漂移系数 显示英文标题

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

摘要： 在本文中，我们研究一类包含乘法分数噪声（Hurts参数为$H > $ 1/2）和高度振荡漂移系数的McKean-Vlasov随机微分方程（SDEs）的平均化原理。 此处对应分数布朗运动的积分是广义的黎曼-斯特尔jes积分。 使用Khasminskii的时间离散化技术，我们证明当时间尺度$ \epsilon $ 趋近于零时，原系统解在上确界和Hölder拓扑下强收敛于平均系统解，这比经典McKean-Vlasov SDE框架中的现有结果更为精确。 显示英文摘要

摘要： 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 $ \epsilon $ gose to zero in the supremum- and H\"older-topologies which are sharpen existing ones in the classical Mckean-Vlasov SDEs framework.