On First-Passage-Time Densities for Certain Symmetric Markov Chains

2004/03/08 by Antonio Di Crescenzo, Di Crescenzo, Antonio, Annapatrizia Nastro +1
Mathematics · #60J27 #60J35 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J27 #msc:60J35

paper · pdf · doi:10.48550/arxiv.math/0403133

10 pages; 1 figure

arxiv created 2004/03/08 · arxiv updated 2009/12/01

Abstract

The spatial symmetry property of truncated birth-death processes studied in Di Crescenzo [6] is extended to a wider family of continuous-time Markov chains. We show that it yields simple expressions for first-passage-time densities and avoiding transition probabilities, and apply it to a bilateral birth-death process with jumps. It is finally proved that this symmetry property is preserved within the family of strongly similar Markov chains.

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