We study the pathwise uniqueness of the solutions to one-dimensional stochastic differential equations driven by Brownian motions and Lévy processes with finite variation paths. The driving Lévy processes are not necessarily one-sided jump processes. In this paper, we obtain some non-Lipschitz conditions on the coefficients, under which the pathwise uniqueness of the solution to the equations is established. Some of our results can be applied to the equation with discontinuous coefficients.

中文翻译：

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由布朗运动和有限变分 Lévy 过程驱动的随机微分方程的路径唯一性

我们研究了由具有有限变化路径的布朗运动和 Lévy 过程驱动的一维随机微分方程解的路径唯一性。驱动 Lévy 过程不一定是片面跳跃过程。在本文中，我们获得了系数的一些非Lipschitz条件，在这些条件下，方程的解的路径唯一性成立。我们的一些结果可以应用于具有不连续系数的方程。