J Austral Math Soc Ser B 37 pp121--144, 1995.

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

Erik A. van Doorn and Pauline Schrijner

Abstract

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.

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Authors

Erik A. van Doorn

Pauline Schrijner

Faculty of Applied Math., University of Twente, 7500 AE Enschede, The Netherlands.