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December, 1961 Markov Renewal Processes with Finitely Many States
Ronald Pyke
Ann. Math. Statist. 32(4): 1243-1259 (December, 1961). DOI: 10.1214/aoms/1177704864


In this paper, Markov Renewal processes having a finite number of states are studied. Explicit expressions are derived for the distribution functions of first passage times, as well as for the marginal distribution function of the corresponding Semi-Markov process. Double generating functions are obtained for the distribution functions of the $N_j$-processes. The limiting behavior of a Markov Renewal process is discussed, the stationary probabilities being derived completely. General Markov Renewal processes are introduced, and a related stationary process is determined. Several examples are given.


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Ronald Pyke. "Markov Renewal Processes with Finitely Many States." Ann. Math. Statist. 32 (4) 1243 - 1259, December, 1961.


Published: December, 1961
First available in Project Euclid: 27 April 2007

zbMATH: 0201.49901
MathSciNet: MR154324
Digital Object Identifier: 10.1214/aoms/1177704864

Rights: Copyright © 1961 Institute of Mathematical Statistics

Vol.32 • No. 4 • December, 1961
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