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Quasistationary distributions for continuous time Markov chains when absorption is not certain

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

P. K. Pollett
P. K. Pollett*
Affiliation:
University of Queensland
*
∗Postal address: Department of Mathematics, The University of Queensland, Brisbane, Queensland 4072, Australia. Email address: pkp@maths.uq.edu.au.
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Abstract

Recently, Elmes et al. (see [2]) proposed a definition of a quasistationary distribution to accommodate absorbing Markov chains for which absorption occurs with probability less than 1. We will show that the probabilistic interpretation pertaining to cases where absorption is certain (see [13]) does not hold in the present context. We prove that the state probabilities at time t conditional on absorption taking place after t, generally depend on t. Conditions are derived under which there is no initial distribution such that the conditional state probabilities are stationary.

Keywords

μ-invariant measuresduality

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J35: Transition functions, generators and resolvents
Type
Short Communications
Information
Journal of Applied Probability , Volume 36 , Issue 1 , March 1999 , pp. 268 - 272
Copyright
Copyright © Applied Probability Trust 1999 

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