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arXiv · 2306.08926

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

Paweł Przybyłowicz·Yue Wu·Xinheng Xie
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Abstract

We investigate existence, uniqueness and approximation of solutions to stochastic delay differential equations (SDDEs) under Carath\'eodory-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 H\"older continuous with respect to the delay variable $z$. We provide a construction of randomized Euler scheme for approximation of solutions of Carath\'eodory SDDEs, and investigate its upper error bound. Finally, we report results of numerical experiments that confirm our theoretical findings.

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Paweł Przybyłowicz, Yue Wu, Xinheng Xie. 2023-06-15. On approximation of solutions of stochastic delay differential equations via randomized Euler scheme. https://arxiv.org/abs/2306.08926

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