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

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)

[thumbnail of Przybylowicz-etal-arXiv-2023-On-approximation-of-solutions-of-stochastic-delay-differential-equations]
Preview
 Text. Filename: Przybylowicz_etal_arXiv_2023_On_approximation_of_solutions_of_stochastic_delay_differential_equations.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo
Download (2MB)| Preview

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.

CORE (COnnecting REpositories)