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February 1997 The quasi-stationary behavior of quasi-birth-and-death processes
N. G. Bean, L. Bright, G. Latouche, C. E. M. Pearce, P. K. Pollett, P. G. Taylor
Ann. Appl. Probab. 7(1): 134-155 (February 1997). DOI: 10.1214/aoap/1034625256


For evanescent Markov processes with a single transient communicating class, it is often of interest to examine the limiting probabilities that the process resides in the various transient states, conditional on absorption not having taken place. Such distributions are known as quasi-stationary (or limiting-conditional) distributions. In this paper we consider the determination of the quasi-stationary distribution of a general level-independent quasi-birth-and-death process (QBD). This distribution is shown to have a form analogous to the matrix-geometric form possessed by the stationary distribution of a positive recurrent QBD. We provide an algorithm for the explicit computation of the quasi-stationary distribution.


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N. G. Bean. L. Bright. G. Latouche. C. E. M. Pearce. P. K. Pollett. P. G. Taylor. "The quasi-stationary behavior of quasi-birth-and-death processes." Ann. Appl. Probab. 7 (1) 134 - 155, February 1997.


Published: February 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0883.60085
MathSciNet: MR1428753
Digital Object Identifier: 10.1214/aoap/1034625256

Primary: 60K25

Keywords: limiting-conditional distribution , Quasi-birth-and-death process , quasi-stationary distribution

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.7 • No. 1 • February 1997
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