Distributions of stopping times for compound poisson processes with positive jumps and linear boundaries

Abstract

Let be a compound Poisson process, i.e. positive random variables and a time homogeneous Poisson jump process. We consider two linear boundaries and and the stopping times and . Laplace Stieltjes transforms are developed for the distributions of TU and T for general distribution of . These transforms are obtained by analyzing the sample path behavior of the process {Yt }. The results are applicable to reliability theory, sequential analysis, queuing theory, dam theory, risk analysis, and more

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