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 [2], we conclude the existence of a unique stationary solution of the exponential Euler scheme that is pathwise asymptotically stable.

翻译：本文讨论了一类具有刚性线性项和由分数布朗运动（fBms）驱动的加性噪声的随机微分方程组，其中赫斯特参数H>1/2，这类方程组来源于随机偏微分方程的空间逼近。针对其数值逼近，我们提出了一种指数欧拉格式，并证明了该格式在强意义下收敛，其确切收敛速率接近赫斯特参数H。此外，基于文献[2]，我们得出指数欧拉格式存在唯一平稳解，该解是路径渐近稳定的。