We discuss a system of stochastic differential equations with a stiff linear term and additive noise driven by fractional Brownian motions (fBms) with Hurst parameter H>1/2, which arise e. g., from spatial approximations of stochastic partial differential equations. For their numerical approximation, we present an exponential Euler scheme and show that it converges in the strong sense with an exact rate close to the Hurst parameter H. Further, based on (E. Buckwar, M.G. Riedler, and P.E. Kloeden 2011), we conclude the existence of a unique stationary solution of the exponential Euler scheme that is pathwise asymptotically stable.

翻译：本文讨论了一类由具有刚性线性项和加性噪声的随机微分方程组成的系统，其噪声由Hurst参数H>1/2的分数布朗运动（fBms）驱动。该系统源于例如随机偏微分方程的空间近似。针对其数值逼近，我们提出了一种指数欧拉格式，并证明该格式在强收敛意义下具有接近Hurst参数H的精确收敛速率。此外，基于（E. Buckwar, M.G. Riedler, and P.E. Kloeden 2011）的研究，我们得出结论：该指数欧拉格式存在唯一的路径渐近稳定平稳解。