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 (2023) On approximation of solutions of stochastic delay differential equations via randomized Euler scheme. Other. arXiv.org, Ithaca, New York. (https://doi.org/10.48550/arXiv.2306.08926)

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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.

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