A review on symmetry properties of birth-death processes

2015/09/08 by Di Crescenzo, Antonio, Martinucci, Barbara
#60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1509.02511

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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