A birth-death process suggested by a chain sequence
type: Item
instance of: scholarly article
title: A birth-death process suggested by a chain sequence
zbMATH Open document ID: 0973.60099
DOI: 10.1016/S0898-1221(00)00157-7
author: R. B. Lenin
author: P. R. Parthasarathy
publication date: 2000-11-13T00:00:00Z
review text: The authors consider a birth-death process on an infinite state whose birth and death rates are suggested by a chain sequence. Using results of constant term chain sequences, explicit expressions involving Chebyshev polynomials are derived for the birth and death rates. Closed form expressions involving the modified Bessel function of the first kind are derived for the transition probabilities and for the time-dependent mean population size. Parallel results are derived for discrete-time birth-death processes. It is shown that both, the continuous-time and the discrete-time birth-death processes are transient and therefore the stationary distribution does not exist.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 1528555
zbMATH Keywords: birth-death processes
zbMATH Keywords: chain sequence
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: Bessel function
zbMATH Keywords: transient behaviour
reviewed by: Annette Kopp-Schneider
MaRDI profile type: Publication
cites work: Q4170993
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full work available at URL: s0898-1221(00)00157-7
OpenAlex ID: W2119228100
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1528555