Successive approximation to solutions of stochastic differential equations with jumps in local non-Lipschitz conditions

In this paper, by using successive approximation, the existence and uniqueness of initial value problem for stochastic differential equations driven by both Wiener process and Poisson process are studied under a local non-Lipschitz conditions. Moreover, the numerical solutions are shown to converge uniformly to the analytical solutions of the stochastic differential equation with jumps.