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

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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, 30 (9). pp. 3222-3242. 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;
  • Item type:Article
    ID code:92411
    Dates:
    Date
    Event
    September 2025
    Published
    1 February 2025
    Published Online
    1 January 2025
    Accepted
    December 2023
    Submitted
    Notes: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:17 Apr 2025 08:24
    URI:https://strathprints.strath.ac.uk/id/eprint/92411
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