Linear implicit approximations of invariant measures of semi-linear SDEs with non-globally Lipschitz coefficients

Pang, Chenxu and Wang, Xiaojie and Wu, Yue (2024) Linear implicit approximations of invariant measures of semi-linear SDEs with non-globally Lipschitz coefficients. Journal of Complexity, 83. 101842. ISSN 1090-2708 (https://doi.org/10.1016/j.jco.2024.101842)

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Abstract

This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler (LTPE) scheme, which also admits an invariant measure, to handle the potential influence of the linear stiffness. Under certain assumptions, both the SDE and the corresponding LTPE method are shown to converge exponentially to the underlying invariant measures, respectively. Moreover, with time-independent regularity estimates for the corresponding Kolmogorov equation, the weak error between the numerical invariant measure and the original one can be guaranteed with convergence of order one. In terms of computational complexity, the proposed ergodicity preserving scheme with the nonlinearity explicitly treated has a significant advantage over the ergodicity preserving implicit Euler method in the literature. Numerical experiments are provided to verify our theoretical findings.

  • Item type:Article
    ID code:88537
    Dates:
    Date
    Event
    31 August 2024
    Published
    21 March 2024
    Published Online
    27 February 2024
    Accepted
    17 September 2023
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:25 Mar 2024 11:01
    Last modified:26 Apr 2024 07:06
    URI:https://strathprints.strath.ac.uk/id/eprint/88537
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