论文标题
由混合分数布朗的粗糙路径驱动的快速慢系统的平均原理
Averaging principle for fast-slow system driven by mixed fractional Brownian rough path
论文作者
论文摘要
本文致力于研究由混合分数布朗式粗糙路径驱动的粗糙微分方程的快速降低系统的平均原理。快速组件是由布朗运动驱动的，而缓慢的组件则由赫斯特索引$ h〜（1/3 <h \ leq 1/2）$驱动。结合了粗糙路径理论的分数演算方法和Khasminskii的经典时间离散方法，我们证明，慢速分量强烈收敛到$ l^1 $ sense中相应平均方程的解。在粗糙路径理论框架中，快速慢系统的平均原理似乎是新的。
This paper is devoted to studying the averaging principle for fast-slow system of rough differential equations driven by mixed fractional Brownian rough path. The fast component is driven by Brownian motion, while the slow component is driven by fractional Brownian motion with Hurst index $H ~(1/3 < H\leq 1/2)$. Combining the fractional calculus approach to rough path theory and Khasminskii's classical time discretization method, we prove that the slow component strongly converges to the solution of the corresponding averaged equation in the $L^1$-sense. The averaging principle for a fast-slow system in the framework of rough path theory seems new.
