mean-square stability and convergence of compensated split-step θ-method for nonlinear jump diffusion systems

In this paper, the existence and uniqueness of the numerical solution of the stochastic differential equations with jumps(sdewjs) under the one side lipschitz conditions and polynomial growth conditions are pre- sented. the compensated split step θ(cssθ) method introduce and try to bound the moment of the numerical solutions also we analyse the strong convergence on the compact domain. we discuss the stability of sdewjs with constant coefficient and prove some new relation between their coefficient. finally, we present three examples to investigate the theories and methods.