First passage times of birth-death processes and simple random walks

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Abstract

It is known that the first passage time of a birth death process from n to n+1 has a completely monotone density, however, the discrete analogue for a simple random walk does not hold. In this paper, first passage times of simple random walks from n to n+1 and from 0 to n are characterized. This discrepancy between the first passage time structures of birth-death process and simple random walks is also analyzed.

Original languageEnglish
Pages (from-to)51-63
Number of pages13
JournalStochastic Processes and their Applications
Volume29
Issue number1
DOIs
Publication statusPublished - 1988

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Keywords

  • birth death processes
  • complete monotonicity
  • generalized phase type distributions
  • simple random walks
  • uniformization

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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