Split-step Method for Stochastic Delay Functional Differential Equations

The Split-step method to stochastic functional differential equations with Poisson jumps and variable delay is introduced in this paper, based on Euler-Maruyama method. And it is proved that the convergence of the Split-step numerical solutions for the stochastic functional differential equations has order 0.5 in the mean-square sense under the global Lipschitz condition, the linear growth condition and the continuity of initial data. Some numerical experiments are simulated to testify the performance and the effectiveness of the method.