First-passage times in skip-free processes

R. L. Tweedie and M. Westcott

Stochastic Processes and their Applications, 1978, vol. 7, issue 2, 191-204

Abstract: We derive simple criteria to ensure the finiteness of the mean first-passage times into semi-infinite sets for real-valued skip-free processes, which move by random jumps in one direction and deterministically, for a random time, in the other. These criteria are applied to state-dependent queueing systems, to give finiteness of the mean of the busy period, and to a self-correcting birth process.

Date: 1978
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