Hitting Time Distributions for Denumerable Birth and Death Processes

Details Hitting Time Distributions for Denumerable Birth and Death Processes Hitting Time Distributions for Denumerable Birth and Death Processes

2010-07-07

arxiv.org/abs/1007.1039v1

Mathematics

Probability

18 pages

Scientific paper

We proved the explicit formulas in Laplace transform of the hitting times for the birth and death processes on a denumerable state space with $\ift$ the exit or entrance boundary. This extends the well known Keilson's theorem from finite state space to infinite state space. We also apply these formulas to the fastest strong stationary time for strongly ergodic birth and death processes, and obtain the explicit convergence rate in separation.

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