In this paper we study jump-diffusion stochastic differential equations (SDEs) with a discontinuous drift coefficient and a possibly degenerate diffusion coefficient. Such SDEs appear in applications such as optimal control problems in energy markets. We prove existence and uniqueness of strong solutions. In addition we study the strong convergence order of the Euler-Maruyama scheme and recover the optimal rate $1/2$.

翻译：在本文中,我们用不连续漂移系数和可能退化的传播系数研究跳跃-扩散随机差异方程式(SDEs),这些SDEs出现在能源市场的最佳控制问题等应用中,我们证明了强有力的解决办法的存在和独特性,此外,我们还研究了欧勒-马鲁山方案强有力的趋同顺序,并恢复了1/2美元的最佳比率。