Strong convergence of Euler-Maruyama schemes for McKean-Vlasov stochastic differential equations under local Lipschitz conditions of state variables

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Li, Yun and Mao, Xuerong and Song, Qingshuo and Wu, Fuke and Yin, George (2023) Strong convergence of Euler-Maruyama schemes for McKean-Vlasov stochastic differential equations under local Lipschitz conditions of state variables. IMA Journal of Numerical Analysis, 43 (2). pp. 1001-1035. ISSN 0272-4979 (https://doi.org/10.1093/imanum/drab107)

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Abstract

This paper develops strong convergence of the Euler-Maruyama (EM) schemes for approximating McKean-Vlasov stochastic differential equations (SDEs). In contrast to the existing work, a novel feature is the use of a much weaker condition-local Lipschitzian in the state variable but under uniform linear growth assumption. To obtain the desired approximation, the paper first establishes the existence and uniqueness of solutions of the original McKean-Vlasov SDE using an Euler-like sequence of interpolations and partition of the sample space. Then, the paper returns to the analysis of the EM scheme for approximating solutions of McKean-Vlasov SDEs. A strong convergence theorem is established. Moreover, the convergence rates under global conditions are obtained.

ORCID iDs

Li, Yun, Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864, Song, Qingshuo, Wu, Fuke and Yin, George;
  • Item type:Article
    ID code:79058
    Dates:
    Date
    Event
    3 April 2023
    Published
    31 January 2022
    Published Online
    21 December 2021
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:23 Dec 2021 09:50
    Last modified:03 Dec 2024 08:07
    URI:https://strathprints.strath.ac.uk/id/eprint/79058
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