In this article we present the compensated two-step Maruyama methods for the stochastic differential equations with Poisson jumps. Mean-square (M-S) order convergence $\frac{1}{2}$ is 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.

中文翻译：

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具有泊松跳跃的随机微分方程的补偿两步 Maruyama 方法

在本文中，我们介绍了具有泊松跳跃的随机微分方程的补偿两步 Maruyama 方法。均方 (MS) 阶收敛$\frac{1}{2}$建立并显示 MS 稳定性分析。特别是，考虑了 Adams 类型的补偿两步 Maruyama 方法，绘制了它们与补偿 Euler-Maruyama 方法 (EM) 相比的线性 MS 稳定性区域。数值结果表明给出了MS收敛性和稳定性。