The two-barrier escape problem for compound renewal processes with two-sided jumps

Abstract

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.