In this paper, we study the numerical method for approximating the random periodic solution of a semiliear stochastic evolution equation with an additive noise. The main challenge lies in proving a convergence over an infinite time horizon while simulating infinite-dimensional objects. We propose a Galerkin-type exponential integrator scheme and establish its convergence rate of the strong error to the mild solution.

翻译：在本文中,我们研究一种数字方法,用一种添加噪声来近似于半利亚尔随机周期性变异变异方程式的随机周期性解决方案。主要挑战在于证明在无限时间跨度上趋同,同时模拟无限维天体。我们提出了一个Galerkin型指数集成器计划,并确定其与温度溶液严重误差的趋同率。