Mean-square convergence and stability of two-step Milstein methods for stochastic differential equations with Poisson jumps

This paper deals with a class of two-step Milstein methods for stochastic differential equations with Poisson jumps. The mean-square convergence and linear mean-square stability of the proposed methods are discussed. In addition, the linear mean-square stability regions of the two-step Milstein methods are compared with those of one-step θ -Milstein methods. Numerical examples demonstrate the mean-square convergence and the linear mean-square stability of the presented methods.