Numerical methods for nonlinear stochastic delay differential equations with jumps

Abstract

In this paper, we modified the split-step backward Euler method (MSSBE) for stochastic delay differential equations with Poisson-driven jumps (SDDEwJs). Second, we prove that MSSBE is strongly convergent if the drift coefficient f(x,y) satisfies one-side Lipschitz with respect to x, global Lipschitz with respect to y, the diffusion and jump coefficients are globally Lipschitz. On the way to proving the convergence result, we show that Euler–Maruyama method converges strongly when SDDEwJs coefficients satisfy local Lipschitz condition, the pth moments of the exact and numerical solution are bounded for some p>2; the MSSBE may be viewed as an Euler–Maruyama approximation to a perturbed SDDEwJs of the same form.