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Quasi-stationary distributions for Markov chains on a general state space

Published online by Cambridge University Press:  14 July 2016

Richard. L. Tweedie
Richard. L. Tweedie*
Affiliation:
The Australian National University, Canberra
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Abstract

The quasi-stationary behaviour of a Markov chain which is φ-irreducible when restricted to a subspace of a general state space is investigated. It is shown that previous work on the case where the subspace is finite or countably infinite can be extended to general chains, and the existence of certain quasi-stationary limits as honest distributions is equivalent to the restricted chain being R-positive with the unique R-invariant measure satisfying a certain finiteness condition.

Keywords

QUASI-STATIONARY DISTRIBUTIONSR-THEORYCONDITIONAL LIMITSGENERAL MARKOV CHAINSRATIO LIMITS
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 726 - 741
Copyright
Copyright © Applied Probability Trust 1974 

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References

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