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Quasi-stationary distributions of birth-and-death processes

Published online by Cambridge University Press:  01 July 2016

James A. Cavender
James A. Cavender*
Affiliation:
Montana State University, Bozeman
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Abstract

Let qn(t) be the conditioned probability of finding a birth-and-death process in state n at time t, given that absorption into state 0 has not occurred by then. A family {q1(t), q2(t), · · ·} that is constant in time is a quasi-stationary distribution. If any exist, the quasi-stationary distributions comprise a one-parameter family related to quasi-stationary distributions of finite state-space approximations to the process.

Keywords

BIRTH-AND-DEATH PROCESSQUASI-STATIONARY DISTRIBUTION
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 3 , September 1978 , pp. 570 - 586
Copyright
Copyright © Applied Probability Trust 1978 

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