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

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:09 Apr 2024 04:28
    URI:https://strathprints.strath.ac.uk/id/eprint/87655
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