We consider the problem of determining two-sided exit probabilities for a compound renewal process with drift and two-sided jumps. In certain cases the problem can be reduced to determining the distribution of a random sum of i.i.d. random variables. In a general situation this problem is reduced to solving a certain integral equation. We obtain explicit expressions for the escape probability for several classes of jump times and sizes.

中文翻译：

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具有两侧跳跃的复合更新过程的双障碍逃逸问题

我们考虑确定具有漂移和两侧跳跃的复合更新过程的两侧退出概率的问题。在某些情况下，问题可以简化为确定独立同分布随机变量的随机和的分布。在一般情况下，这个问题被简化为求解某个积分方程。我们获得了几类跳跃时间和大小的逃逸概率的显式表达式。