The random periodic solution of a stochastic differential equation with a monotone drift and its numerical approximation

2021/05/27 by Wu, Yue
#37H99 #60H10 #60H35 #65C30 #65L04 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2105.13477

Abstract

In this paper we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler-Maruyama method. The existence of the random periodic solution is shown as the limits of the pull-back flows of the SDE and discretized SDE respectively. We establish a convergence rate of the strong error for the backward Euler-Maruyama method and obtain the weak convergence result for the approximation of the periodic measure.

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