Hitting Time Distributions for Denumerable Birth and Death Processes

2010/07/07 by Yu Gong, Gong, Yu, Yong-Hua Mao +1 · 1 citation
Business, Management and Accounting · Mathematics · Physics and Astronomy · #37A30 #47A75 #60J27 #60J35 #Advanced Queuing Theory Analysis #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1007.1039

openalex publication_date 2010/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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