The semi-implicit Euler method for stochastic differential delay equation with jumps

The class of jump-diffusion SDDEs that admits explicit solutions is rather limited. Consequently, there is a need for the systematic use of discrete time approximations in corresponding simulations. In this paper, we shall deal with convergence of the semi-implicit Euler method for Nonlinear stochastic differential delay equation driven by Wiener processes and Poisson processes. It is proved that the semi-implicit Euler method is convergent with strong order p=12.