GEOMETRIC ERGODICITY AND QUASI-STATIONARITY IN

DISCRETE-TIME BIRTH-DEATH PROCESSES

ERIK A. VAN DOORN AND PAULINE SCHRIJNER

Faculty of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

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, condtions 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 nstep transition probabilities of a birth-death process developed by Karlin and McGregor.

AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60J80