We show that the comparison results for a backward SDE with jumps established in Royer (Stoch. Process. Appl 116: 1358–1376, 2006) and Yin and Mao (J. Math. Anal. Appl 346: 345–358, 2008) hold under more simplified conditions. Moreover, we prove existence and uniqueness allowing the coefficients in the linear growth- and monotonicity-condition for the generator to be random and time-dependent. In the L2-case with linear growth, this also generalizes the results of Kruse and Popier (Stochastics 88: 491–539, 2016). For the proof of the comparison result, we introduce an approximation technique: Given a BSDE driven by Brownian motion and Poisson random measure, we approximate it by BSDEs where the Poisson random measure admits only jumps of size larger than 1/n.

中文翻译：

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扩展单调生成器设置中具有 Lévy 跳跃的 BSDE 的存在性、唯一性和比较结果。

我们表明，在 Royer (Stoch. Process. Appl 116: 1358–1376, 2006) 和 Yin and Mao (J. Math. Anal. Appl 346: 345–358, 2008) 中建立了跳跃的后向 SDE 的比较结果成立在更简化的条件下。此外，我们证明存在性和唯一性允许生成器的线性增长和单调性条件中的系数是随机的和时间相关的。在线性增长的 L2 情况下，这也概括了 Kruse 和 Popier 的结果（Stochastics 88: 491–539, 2016）。为了证明比较结果，我们引入了一种近似技术：给定一个由布朗运动和泊松随机测度驱动的 BSDE，我们通过泊松随机测度仅允许大小大于 1/n 的跳跃的 BSDE 对其进行近似。