Quasistationarity in continuous time Markov chains where absorption is not certain

Darlington, S.J. and Pollett, P.K.

Abstract: In a recent paper it was shown that, for an absorbing Markov chain where absorption is not guaranteed, the state probabilities at time t conditional on non-absorption by t generally depend on t. Conditions were derived under which there can be no initial distribution such that the conditional state probabilities are stationary. The purpose of this note is to show that these conditions can be relaxed completely: we prove, once and for all, that there are no circumstances under which a quasistationary distribution can admit a stationary conditional interpretation.

Keywords: mu-invariant measures; duality

Acknowledgement: This worked was funded by the Australian Research Council.

The authors:

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

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Last modified: 28th January 1997