The Annals of Probability

Equilibrium Measures for Semi-Markov Processes

David R. McDonald

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Abstract

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: $$(\mathbf{I}_{(t)}, \mathbf{Z}_{(t)}) = \text{(last state entered before time t}$$, $$\text{duration of this last sojourn up to} t$$).

Article information

Source
Ann. Probab., Volume 5, Number 5 (1977), 818-822.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995726

Digital Object Identifier
doi:10.1214/aop/1176995726

Mathematical Reviews number (MathSciNet)
MR455142

Zentralblatt MATH identifier
0386.60066

JSTOR
links.jstor.org

Subjects
Primary: 60K05: Renewal theory
Secondary: 60K15: Markov renewal processes, semi-Markov processes 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60B99: None of the above, but in this section

Keywords
Semi-Markov equilibrium measure

Citation

McDonald, David R. Equilibrium Measures for Semi-Markov Processes. Ann. Probab. 5 (1977), no. 5, 818--822. doi:10.1214/aop/1176995726. https://projecteuclid.org/euclid.aop/1176995726


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