It is now known that, under a weaker condition than the Lipschitz one, the existence and uniqueness result for solutions of stochastic differential equations driven simultaneously by a fractional Brownian motion with Hurst parameter $H>1∕2$ and a standard Brownian motion is obtained. Therefore, it is quite natural to ask whether or when the averaging principle result also holds. In this paper we study this problem using the tool of generalized Stieltjes integral and Bihari-type lemma.

中文翻译：

---

混合随机微分方程：平均原理结果

现已知道，在比Lipschitz条件弱的条件下，由具有Hurst参数的分数布朗运动同时驱动的随机微分方程解的存在性和唯一性结果 $H>\mathrm{1个}∕2$并获得标准的布朗运动。因此，很自然地要问平均原理结果是否或何时成立。在本文中，我们使用广义Stieltjes积分和Bihari型引理研究该问题。