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Quasi-stationary distributions in semi-Markov processes

Published online by Cambridge University Press:  14 July 2016

C. K. Cheong
C. K. Cheong*
Affiliation:
University of Malaya
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Abstract

Our main concern in this paper is the convergence, as t → ∞, of the quantities i, j ∈ E; where Pij(t) is the transition probability of a semi-Markov process whose state space E is irreducible but not closed (i.e., escape from E is possible), and rj is the probability of eventual escape from E conditional on the initial state being i. The theorems proved here generalize some results of Seneta and Vere-Jones ([8] and [11]) for Markov processes.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 388 - 399
Copyright
Copyright © Applied Probability Trust 1970 

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References

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