First passage times and lumpability of semi-Markov processes
- 1 March 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 25 (04) , 675-687
- https://doi.org/10.1017/s0021900200041462
Abstract
A necessary and sufficient condition of Serfozo (1971) for lumpability of semi-Markov processes is reinterpreted in terms of first-exit times. Furthermore, a new necessary and sufficient condition is developed by establishing relationships between first-passage times and lumpability of semi-Markov processes. The approach taken in this paper is entirely based on the Laplace-transform domain.Keywords
This publication has 9 references indexed in Scilit:
- Weak lumpability in finite Markov chainsJournal of Applied Probability, 1982
- Technical Note—An Eigenvector Condition for Markov Chain LumpabilityOperations Research, 1977
- An Approximate Test of Markov Chain LumpabilityJournal of the American Statistical Association, 1977
- Exceptional Paper—Markov Renewal Theory: A SurveyManagement Science, 1975
- Functions of Semi-Markov ProcessesSIAM Journal on Applied Mathematics, 1971
- Markov renewal theoryAdvances in Applied Probability, 1969
- Decomposition of a Semi-Markov Process Under a State Dependent RuleSIAM Journal on Applied Mathematics, 1967
- DECOMPOSITION OF A SEMI‐MARKOV PROCESS UNDER A MARKOVIAN RULEAustralian Journal of Statistics, 1966
- A Markovian Function of a Markov ChainThe Annals of Mathematical Statistics, 1958