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

Antonio Di Crescenzo; Annapatrizia Nastro

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

Antonio Di Crescenzo·Annapatrizia Nastro

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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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Antonio Di Crescenzo, Annapatrizia Nastro. 2004-03-08. On First-Passage-Time Densities for Certain Symmetric Markov Chains. https://arxiv.org/abs/math/0403133

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