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Some results for quasi-stationary distributions of birth-death processes

Published online by Cambridge University Press:  14 July 2016

Masaaki Kijima  and
E. Seneta
Masaaki Kijima*
Affiliation:
The University of Tsukuba, Tokyo
E. Seneta*
Affiliation:
University of Sydney
*
∗ Postal address: Graduate School of Systems Management, The University of Tsukuba, Tokyo, Otsuka, Bunkyo-ku, Tokyo 112, Japan.
∗∗ Postal address: Department of Mathematical Statistics, University of Sydney, Sydney, NSW 2006, Australia.
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Abstract

Quasi-stationary distributions are considered in their own right, and from the standpoint of finite approximations, for absorbing birth-death processes. Results on convergence of finite quasi-stationary distributions and a stochastic bound for an infinite quasi-stationary distribution are obtained. These results are akin to those of Keilson and Ramaswamy (1984). The methodology is a synthesis of Good (1968) and Cavender (1978).

Keywords

INVARIANT MEASURESORTHOGONAL POLYNOMIALSSTOCHASTIC BOUNDSTRUNCATIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 503 - 511
Copyright
Copyright © Applied Probability Trust 1991 

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