On approximation of solutions of stochastic delay differential equations via randomized Euler scheme

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Przybyłowicz, Paweł and Wu, Yue and Xie, Xinheng (2024) On approximation of solutions of stochastic delay differential equations via randomized Euler scheme. Applied Numerical Mathematics, 197. pp. 143-163. ISSN 0168-9274 (https://doi.org/10.1016/j.apnum.2023.11.008)

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Abstract

We investigate existence, uniqueness and approximation of solutions to stochastic delay differential equations (SDDEs) under Carathéodory-type drift coefficients. Moreover, we also assume that both drift f=f(t,x,z) and diffusion g=g(t,x,z) coefficient are Lipschitz continuous with respect to the space variable x, but only Hölder continuous with respect to the delay variable z. We provide a construction of randomized Euler scheme for approximation of solutions of Carathéodory SDDEs, and investigate its upper error bound. Finally, we report results of numerical experiments that confirm our theoretical findings.

  • Item type:Article
    ID code:87655
    Dates:
    Date
    Event
    31 March 2024
    Published
    24 November 2023
    Published Online
    12 November 2023
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:18 Dec 2023 10:51
    Last modified:25 Nov 2024 01:43
    URI:https://strathprints.strath.ac.uk/id/eprint/87655
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