Split-Step Method for Nonlinear Stochastic Delay Differential Equation with Jumps

This paper discusses split step algorithm for solving nonlinear stochastic delay differential equation with jumps in It sense. It is proved that the split step method is uniformly convergent with order of 1.5 in the mean sense and order of 1 in the mean square sense. The mean square stable of the split step method under some conditions is also obtained. Some numerical experiments are reported to testify the performance and effectiveness of this method in this paper.