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In this article we present the compensated two-step Maruyama methods for the stochastic differential equations with Poisson jumps. Mean-square (M-S) order convergenceis established and M-S stability analysis are displayed. In particular, compensated two-step Maruyama methods of Adams type are considered, their linear M-S stability regions compared with compensated Euler–Maruyama method (EM) are plotted. Numerical results show the M-S convergence and stability are given.

Compensated two-step Maruyama methods for stochastic differential equations with Poisson jumps