The random periodic solution of a stochastic differential equation with a monotone drift and its numerical approximation
Probability
2021-08-19 v4
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.
Keywords
Cite
@article{arxiv.2105.13477,
title = {The random periodic solution of a stochastic differential equation with a monotone drift and its numerical approximation},
author = {Yue Wu},
journal= {arXiv preprint arXiv:2105.13477},
year = {2021}
}