Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime

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. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we design numerical schemes for a class of slow-fast systems of stochastic differential equations. The proposed scheme exhibits an asymptotic preserving property, where a limiting scheme consistent with the averaged equation is obtained as the time-scale parameter approaches 0. The authors also illustrate the recently proved averaging result for the considered SDE systems and highlight the main differences compared to the standard Wiener case.