Quasi-stationary distributions for birth-death processes with killing
type: Item
instance of: scholarly article
title: Quasi-stationary distributions for birth-death processes with killing
zbMATH Open document ID: 1147.60323
DOI: 10.1155/JAMSA/2006/84640
author: Pauline Coolen-Schrijner
author: Erik A. van Doorn
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2008-08-15T00:00:00Z
full work available at URL: https://eudml.org/doc/54626
review text: Summary: The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state (killing) is possible from any state rather than just one state. The purpose of this paper is to investigate to what extent properties of birth-death processes, in particular with regard to the existence of quasi-stationary distributions, remain valid in the generalized setting. It turns out that the elegant structure of the theory of quasi-stationarity for birth-death processes remains largely intact as long as killing is possible from only finitely many states. In particular, the existence of a quasi-stationary distribution is ensured in this case if absorption is certain and the state probabilities tend to zero exponentially fast.
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 5312408
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5312408