Order-one convergence of the backward Euler method for random periodic solutions of semilinear SDEs

Guo, Yujia and Wang, Xiaojie and Wu, Yue (2025) Order-one convergence of the backward Euler method for random periodic solutions of semilinear SDEs. Discrete and Continuous Dynamical Systems - Series B. ISSN 1531-3492 (https://doi.org/10.3934/dcdsb.2025018)

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Abstract

In this paper, we revisit the backward Euler method for numerical approximations of random periodic solutions of semilinear SDEs with additive noise. Improved Lp-estimates of the random periodic solutions of the considered SDEs are obtained under a more relaxed condition compared to literature. The backward Euler scheme is proved to converge with an order one in the mean square sense, which also improves the existing order-half convergence. Numerical examples are presented to verify our theoretical analysis.

ORCID iDs

Guo, Yujia, Wang, Xiaojie and Wu, Yue ORCID logoORCID: https://orcid.org/0000-0002-6281-2229;