Quasi-stationary distributions for Markov chains on a general state space
- 1 December 1974
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 11 (4) , 726-741
- https://doi.org/10.2307/3212556
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
This publication has 10 references indexed in Scilit:
- $R$-Theory for Markov Chains on a General State Space I: Solidarity Properties and $R$-Recurrent ChainsThe Annals of Probability, 1974
- On the quasi-stationary distribution of the virtual waiting time in queues with Poisson arrivalsJournal of Applied Probability, 1971
- On the quasi-stationary distribution of the virtual waiting time in queues with Poisson arrivalsJournal of Applied Probability, 1971
- Compactness and sequential compactness in spaces of measuresProbability Theory and Related Fields, 1971
- Ergodic properties of nonnegative matrices. IPacific Journal of Mathematics, 1967
- On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of statesJournal of Applied Probability, 1966
- On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of statesJournal of Applied Probability, 1966
- On Quasi-Stationary distributions in absorbing discrete-time finite Markov chainsJournal of Applied Probability, 1965
- On Quasi-Stationary distributions in absorbing discrete-time finite Markov chainsJournal of Applied Probability, 1965
- GEOMETRIC ERGODICITY IN DENUMERABLE MARKOV CHAINSThe Quarterly Journal of Mathematics, 1962