An explicit approximation for super-linear stochastic functional differential equations

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Li, Xiaoyue and Mao, Xuerong and Song, Guoting (2024) An explicit approximation for super-linear stochastic functional differential equations. Stochastic Processes and their Applications, 169. 104275. ISSN 0304-4149 (https://doi.org/10.1016/j.spa.2023.104275)

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Abstract

Since it is difficult to implement implicit schemes on the infinite-dimensional space, we aim to develop the explicit numerical method for approximating super-linear stochastic functional differential equations (SFDEs). Precisely, borrowing the truncation idea and linear interpolation we propose an explicit truncated Euler–Maruyama (EM) scheme for SFDEs, and obtain the boundedness and convergence in Lp (p≥2). We also prove the convergence rate with 1/2 order. Different from some previous works (Mao, 2003; Zhang et al., 2018), we release the global Lipschitz restriction on the diffusion coefficient. Furthermore, we reveal that numerical solutions preserve the underlying exponential stability. Moreover, we give several examples to support our theory.

ORCID iDs

Li, Xiaoyue, Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864 and Song, Guoting;
  • Item type:Article
    ID code:87712
    Dates:
    Date
    Event
    31 March 2024
    Published
    18 December 2023
    Published Online
    13 December 2023
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:21 Dec 2023 16:22
    Last modified:18 Dec 2024 02:31
    URI:https://strathprints.strath.ac.uk/id/eprint/87712
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