Strong Convergence of the Split-Step Theta Method for Stochastic Delay Differential Equations with Nonglobally Lipschitz Continuous Coefficients

Abstract

This paper is concerned with the convergence analysis of numerical methods for stochastic delay differential equations. We consider the split-step theta method for nonlinear nonautonomous equations and prove the strong convergence of the numerical solution under a local Lipschitz condition and a coupled condition on the drift and diffusion coefficients. In particular, these conditions admit that the diffusion coefficient is highly nonlinear. Furthermore, the obtained results are supported by numerical experiments.