Order-One Convergence of the Backward Euler Method for Random Periodic Solutions of Semilinear SDEs

06/11/2023
by   Yujia Guo, et al.
0

In this paper, we revisit the backward Euler method for numerical approximations of random periodic solutions of semilinear SDEs with additive noise. The existence and uniqueness of the random periodic solution are discussed as the limit of the pull-back flows of SDEs under a relaxed condition compared to literature. The backward Euler scheme is proved to converge with an order one in the mean square sense, which improves the existing order-half convergence. Numerical examples are presented to verify our theoretical analysis.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset