Escape and survival probabilities for compound renewal processes with drift are reduced to integral equations and solved for Erlang(n), hypo-exponential, and rational Laplace transform interarrival distributions in the one-sided jump case, with some two-sided cases identified.
Duan 2015, An Introduction to Stochastic Dynamics 2, Cambridge Uni- versity Press, New York
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Escape probabilities of compound renewal processes with drift
Escape and survival probabilities for compound renewal processes with drift are reduced to integral equations and solved for Erlang(n), hypo-exponential, and rational Laplace transform interarrival distributions in the one-sided jump case, with some two-sided cases identified.