A review on symmetry properties of birth-death processes

Antonio Di Crescenzo; Barbara Martinucci

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arXiv · 1509.02511

A review on symmetry properties of birth-death processes

Antonio Di Crescenzo·Barbara Martinucci

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Abstract

In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the transition rates such that the transition probabilities satisfy a spatial symmetry relation. The latter leads to simple expressions for first-passage-time densities and avoiding transition probabilities. This approach is thus thoroughly extended to the case of bilateral birth-death processes, even in the presence of catastrophes, and to the case of a two-dimensional birth-death process with constant rates.

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Antonio Di Crescenzo, Barbara Martinucci. 2015-09-08. A review on symmetry properties of birth-death processes. https://arxiv.org/abs/1509.02511

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