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

Pollett, P.K.

Abstract: Recently, Elmes, Pollett and Walker 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 (van Doorn) 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: mu-invariant measures; duality

Acknowledgements: This research was supported by the Australia Research Council (Grant No. A69130032).

The author:

• Phil Pollett, Discipline of Mathematics, The University of Queensland. pkp@maths.uq.edu.au

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Last modified: 16th January 1998