A note on integrals for birth-death processes
type: Item
instance of: scholarly article
title: A note on integrals for birth-death processes
zbMATH Open document ID: 0968.92019
DOI: 10.1016/S0025-5564(00)00046-8
author: Valeri T. Stefanov
author: Song Wang
published in: Mathematical Biosciences
publication date: 2001-07-17T00:00:00Z
review text: A general integral for birth-death Markov processes until the time of extinction is considered. A closed form expression is provided for the expected value in terms of birth and death rates. Several examples are provided: the M/M/1 queue, the M/M/\(\infty\) queue, the linear birth-death process, and the stochastic logistics SIS epidemic. A simple route for numerical evaluation of the integral variance is also suggested. This is a generalization and correction of an article of \textit{C.M. Hernandez-Suarez} and \textit{C. Castillo-Chavez} [ibid. 161, No.1-2, 95-104 (1999; Zbl 0938.60056)].
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 1563821
zbMATH Keywords: birth-death processes
zbMATH Keywords: hitting time
zbMATH Keywords: integrals of Markov processes
Wikidata QID: Q52070005
reviewed by: Valentin Topchii
MaRDI profile type: Publication
cites work: A basic result on the integral for birth-death Markov processes
cites work: Mean passage times for tridiagonal transition matrices
cites work: Modelling Biological Populations in Space and Time
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description: scientific article; zbMATH DE number 1563821