Convergence Analysis of a Splitting Method for Stochastic Differential Equations

Abstract

In this paper, we propose a fully drift-implicit splitting numerical scheme for the stochastic differential equations driven by the standard $d$-dimensional Brownian motion. We prove that its strong convergence rate is of the same order as the standard Euler-Maruyama method. Some numerical experiments are also carried out to demonstrate this property. This scheme allows us to use the latest information inside each iteration in the Euler-Maruyama method so that better approximate solutions could be obtained than the standard approach.