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

Yujia Guo; Xiaojie Wang; Yue Wu

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arXiv · 2306.06689

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

Yujia Guo·Xiaojie Wang·Yue Wu

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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 $L^{p}$-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.

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BibTeX RIS

Yujia Guo, Xiaojie Wang, Yue Wu. 2023-06-11. Order-One Convergence of the Backward Euler Method for Random Periodic Solutions of Semilinear SDEs. https://arxiv.org/abs/2306.06689

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