A basic result on the integral for birth-death Markov processes
type: Item
instance of: scholarly article
title: A basic result on the integral for birth-death Markov processes
zbMATH Open document ID: 0938.60056
DOI: 10.1016/S0025-5564(99)00034-6
author: Carlos Castillo-Chavez
author: Carlos M. Hernandez-Suarez
published in: Mathematical Biosciences
publication date: 1999-11-25T00:00:00Z
review text: This paper is concerned with the expectation of the integral under the stochastic path of a birth-death Markov process until its time of extinction. It also considers the expected time to extinction. The argument used is a regenerative one. 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 table of values for both the integral under the path until extinction, and the expected time to extinction in the SIS epidemic is provided for different values of the birth and death parameters. The paper concludes with two appendices and a list of 22 references.
reviewed by: J. Gani
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 1369602
zbMATH Keywords: absorbing Markov processes
zbMATH Keywords: birth-death processes
zbMATH Keywords: queueing theory
zbMATH Keywords: integrals of Markov processes
MaRDI profile type: Publication
Wikidata QID: Q52138754
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full work available at URL: s0025-5564(99)00034-6
OpenAlex ID: W2138635628
description: scientific article; zbMATH DE number 1369602