标题： 平均原理对于第三级粗糙慢快系统 显示英文标题

标题： Averaging principle for rough slow-fast systems of level 3

摘要： 各种随机（偏）微分方程的慢快系统平均原理已经被广泛研究。几年前，类似的结果被证明适用于由随机粗糙路径驱动的粗糙微分方程慢快系统，并且“粗糙慢快系统”的研究似乎正在获得更多的关注。然而，在所有已知的结果中，驱动的粗糙路径均为二阶。本文我们提出了由三阶随机粗糙路径驱动的粗糙慢快系统，并证明了Khas'minskii型强平均原理。 显示英文摘要

摘要： The averaging principle for slow-fast systems of various kind of stochastic (partial) differential equations has been extensively studied. An analogous result was shown for slow-fast systems of rough differential equations driven by random rough paths a few years ago and the study of ``rough slow-fast systems" seems to be gaining momentum now. In all known results, however, the driving rough paths are of level 2. In this paper we formulate rough slow-fast systems driven by random rough paths of level 3 and prove the strong averaging principle of Khas'minskii-type.