Abstract In this paper, we present and analyze a compensated projected Euler-Maruyama method for stochastic differential equations with jumps. A mean square convergence result is derived under a coupled condition. This condition and some reasonable assumptions admit that the jump and diffusion coefficients can be superlinear. Moreover, since the Poisson increment has different moment properties from the Brownian increment, some new techniques are developed for convergence analysis. Finally, some numerical experiments are carried out to confirm the theoretical results.

中文翻译：

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具有超线性跳跃的随机微分方程的补偿投影 Euler-Maruyama 方法

摘要 在本文中，我们提出并分析了带跳跃的随机微分方程的补偿投影欧拉-丸山方法。在耦合条件下导出均方收敛结果。这个条件和一些合理的假设承认跳跃和扩散系数可以是超线性的。此外，由于泊松增量与布朗增量具有不同的矩特性，因此开发了一些用于收敛分析的新技术。最后，进行了一些数值实验来验证理论结果。