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Geomatric ergodicity and quasi-stationarity in discrete-time birth-death processes

Published online by Cambridge University Press:  17 February 2009

Erik A. van Doorn  and
Pauline Schrijner
Erik A. van Doorn
Affiliation:
Faculty of Applied Math., University of Twente, 7500 AE Enschede, The Netherlands.
Pauline Schrijner
Affiliation:
Faculty of Applied Math., University of Twente, 7500 AE Enschede, The Netherlands.
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Abstract

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We study two aspects of discrete-time birth-death processes, the common feature of which is the central role played by the decay parameter of the process. First, conditions for geometric ergodicity and bounds for the decay parameter are obtained. Then the existence and structure of quasi-stationary distributions are discussed. The analyses are based on the spectral representation for the n-step transition probabilities of a birth-death process developed by Karlin and McGregor.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 2 , October 1995 , pp. 121 - 144
Copyright
Copyright © Australian Mathematical Society 1995

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