The Galerkin analysis for the random periodic solution of semilinear stochastic evolution equations

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.