标题： 几乎必然平均化对于由分数布朗运动驱动的演化方程 显示英文标题

标题： Almost Sure Averaging for Evolution Equations driven by fractional Brownian motions

摘要： 我们将平均方法应用于由两个演化方程组成的耦合系统，该系统有一个由分数布朗运动（FBM）驱动的慢分量，其赫斯特参数为$H_1> \frac12$，以及一个由加性 FBM 驱动的快分量，其赫斯特参数为$ H_2\in(1-H_1,1)$。主要目的是证明此类耦合系统的慢分量可以由具有平均系数的随机演化方程来描述。我们的第一个结果为混合随机演化方程组提供了路径意义下的弱解。我们的主要结果涉及一种平均过程，该过程通过时间离散化的方法证明了慢分量几乎必然收敛到相应平均方程的解。为此，我们通过由快分量生成的随机动力系统的一个指数吸引的随机不动点生成一个平稳解。 显示英文摘要

摘要： We apply the averaging method to a coupled system consisting of two evolution equations which has a slow component driven by fractional Brownian motion (FBM) with the Hurst parameter $H_1> \frac12$ and a fast component driven by additive FBM with the Hurst parameter $ H_2\in(1-H_1,1)$. The main purpose is to show that the slow component of such a couple system can be described by a stochastic evolution equation with averaged coefficients. Our first result provides a pathwise mild solution for the system of mixed stochastic evolution equations. Our main result deals with an averaging procedure which proves that the slow component converges almost surely to the solution of the corresponding averaged equation using the approach of time discretization. To do this we generate a stationary solution by a exponentially attracting random fixed point of the random dynamical system generated by the fast component.