Equilibrium Measures for Semi-Markov Processes

This paper simplifies and extends previous results on the existence of an equilibrium or stationary measure for the age process associated with a semi-Markov chain: $$(\mathbf{I}_{(t)}, \mathbf{Z}_{(t)}) = \text{(last state entered before time t}$$, $$\text{duration of this last sojourn up to} t$$).

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Bibliographic Details
Published in:The Annals of probability 1977-10, Vol.5 (5), p.818-822
Main Author: McDonald, David R.
Format: Article
Language:English
Subjects:
60B99
60J10
60K05
60K15
Integers
Markov chains
Mathematics
Semi-Markov equilibrium measure
Short Communications
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Description
Summary:This paper simplifies and extends previous results on the existence of an equilibrium or stationary measure for the age process associated with a semi-Markov chain: $$(\mathbf{I}_{(t)}, \mathbf{Z}_{(t)}) = \text{(last state entered before time t}$$, $$\text{duration of this last sojourn up to} t$$).
ISSN:0091-1798
2168-894X
DOI:10.1214/aop/1176995726