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 semiliear stochastic evolution equations. 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.