论文标题
通过受控路径平均粗略方程的慢速系统的原理
Averaging principle for slow-fast systems of rough differential equations via controlled paths
论文作者
论文摘要
在本文中，我们证明了一个慢速差分方程的慢速系统的强大平均原理。系统的慢组分和快速组件分别由一条相当一般的随机粗糙路径和布朗的粗糙路径驱动。假定这两个驾驶噪声是独立的。慢组分驱动器的一个突出例子是赫斯特参数在1/3到1/2之间的分数布朗式粗糙路径。我们在受控路径理论的框架中工作，这是粗糙路径理论中最广泛使用的框架之一。为了证明我们的主要定理，我们在此框架中执行了Khas'Minskii的时间限制方法。
In this paper we prove the strong averaging principle for a slow-fast system of rough differential equations. The slow and the fast component of the system are driven by a rather general random rough path and Brownian rough path, respectively. These two driving noises are assumed to be independent. A prominent example of the driver of the slow component is fractional Brownian rough path with Hurst parameter between 1/3 and 1/2. We work in the framework of controlled path theory, which is one of the most widely-used frameworks in rough path theory. To prove our main theorem, we carry out Khas'minskii's time-discretizing method in this framework.
