Birth and death processes with absorption
type: Item
instance of: scholarly article
title: Birth and death processes with absorption
zbMATH Open document ID: 0758.60072
DOI: 10.1155/S0161171292000632
author: Mourad E. H. Ismail
author: Jean Letessier
author: Galliano Valent
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/46762
review text: In a stationary birth and death process with birth rates \(\{\lambda_ n\}\) and death rates \(\{\mu_ n\}\), there is a long established spectral representation for the transition probabilities in the case where \(\lambda_ n>0\) for \(n\geq 0\) and \(\mu_ n>0\) for \(n\geq 1\), due to \textit{S. Karlin} and \textit{J. McGregor} [Trans. Am. Math. Soc. 85, 489-546 (1957)]. Here the case \(\lambda_ 0=0\) is covered by a careful study of what happens as \(\lambda_ 0\) tends to zero from above in the Karlin- McGregor representation. Some examples are discussed, and an inequality for Dirichlet polynomials is deduced.
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 89241
zbMATH Keywords: birth and death process
zbMATH Keywords: spectral representation
zbMATH Keywords: Karlin-McGregor representation
zbMATH Keywords: Dirichlet polynomials
reviewed by: D. R. Grey
MaRDI profile type: Publication
OpenAlex ID: W2164287785
description: scientific article; zbMATH DE number 89241