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

06/15/2023

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by   Paweł Przybyłowicz, et al.

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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.