Additional quasi-stationary distributions for semi-Markov processes
- 1 June 1972
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 9 (3) , 671-676
- https://doi.org/10.2307/3212336
Abstract
Consider a semi-Markov process X(t) defined on a subset of the non-negative integers with zero as an absorbing state and the non-zero states forming an irreducible class with exit to zero being possible. Conditions are given for the existence of the limits: where Xj(t) is the amount of time prior to time t spent in state j.The limits (which are independent of the initial state) are evaluated when the sufficient conditions are satisfied.Keywords
This publication has 6 references indexed in Scilit:
- Quasi-stationary distributions in semi-Markov processesJournal of Applied Probability, 1970
- Ergodic and ratio limit theorems for ?-recurrent semi-Markov processesProbability Theory and Related Fields, 1968
- On quasi-stationary distributions in absorbing continuous-time finite Markov chainsJournal of Applied Probability, 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 absorbing discrete-time finite Markov chainsJournal of Applied Probability, 1965
- Limit Theorems for Markov Renewal ProcessesThe Annals of Mathematical Statistics, 1964