Some recent results on the distributions of stopping times of compound Poisson processes with linear boundaries

A review of recent results is given, for the distribution of stopping times defined on compound Poisson processes and linear boundaries. Generalization of the results of Zacks (Commun. Statist. Stochastic Models 7 (1991) 233) is given for discrete compound Poisson processes. The main approach in the reviewed papers is that of sample path analysis, which leads to renewal type equations. Explicit solutions are given.