Hitting time distribution for skip-free Markov chains: A simple proof

Ke Zhou

Statistics & Probability Letters, 2013, vol. 83, issue 7, 1782-1786

Abstract: A well-known theorem for an irreducible skip-free Markov chain on the nonnegative integers with absorbing state d, under some conditions, is that the hitting (absorbing) time of state d starting from state 0 is distributed as the sum of d independent geometric (or exponential) random variables. The purpose of this paper is to present a direct and simple proof of the theorem in the cases of both discrete and continuous time skip-free Markov chains. Our proof is to calculate directly the generation functions (or Laplace transforms) of hitting times in terms of the iteration method.

Keywords: Skip-free; Random walk; Birth and death chain; Hitting time; Recurrence equation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2013.04.008

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