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
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Item type: Article ID code: 92411 Dates: DateEvent1 February 2025Published1 February 2025Published Online1 January 2025AcceptedDecember 2023SubmittedNotes: This article has been published in a revised form in Discrete and Continuous Dynamical Systems - Series B: https://doi.org/10.3934/dcdsb.2025018. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works. Subjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 20 Mar 2025 15:44 Last modified: 20 Mar 2025 15:44 URI: https://strathprints.strath.ac.uk/id/eprint/92411