We design numerical schemes for a class of slow-fast systems of stochastic differential equations, where the fast component is an Ornstein-Uhlenbeck process and the slow component is driven by a fractional Brownian motion with Hurst index $H>1/2$. We establish the asymptotic preserving property of the proposed scheme: when the time-scale parameter goes to $0$, a limiting scheme which is consistent with the averaged equation is obtained. With this numerical analysis point of view, we thus illustrate the recently proved averaging result for the considered SDE systems and the main differences with the standard Wiener case.

翻译：我们设计了一组慢速慢速软体差异方程式的计算方法,即快速元件为Ornstein-Uhlenbeck进程,慢元件由部分布朗运动驱动,Hurst 指数为$H>1/2美元。我们建立了拟议办法的无保护属性:当时间尺度参数达到0美元时,将获得一个与平均方程式一致的限制方案。用这一数字分析观点,我们由此说明了最近证明的经过考虑的SDE系统平均结果,以及标准Wiener案的主要差异。