Backward Euler–Maruyama method for the random periodic solution of a stochastic differential equation with a monotone drift

Wu, Yue (2022) Backward Euler–Maruyama method for the random periodic solution of a stochastic differential equation with a monotone drift. Journal of Theoretical Probability, 36 (1). pp. 605-622. ISSN 0894-9840 (https://doi.org/10.1007/s10959-022-01178-w)

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Abstract

In this paper, we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler–Maruyama method. The existence of the random periodic solution is shown as the limit of the pull-back flows of the SDE and the discretized SDE, respectively. We establish a convergence rate of the strong error for the backward Euler–Maruyama method with order of convergence 1/2.

  • Item type:Article
    ID code:80667
    Dates:
    Date
    Event
    11 May 2022
    Published
    9 April 2022
    Accepted
    18 October 2021
    Submitted
    Notes:This work is supported by the Alan Turing Institute for funding this work under EPSRC Grant EP/N510129/1 and EPSRC for funding though the Project EP/S026347/1, titled "Unparameterised multimodal data, high order signatures, and the mathematics of data science."
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:12 May 2022 09:50
    Last modified:16 Apr 2024 02:52
    URI:https://strathprints.strath.ac.uk/id/eprint/80667
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