## The Annals of Mathematical Statistics

### Markov Renewal Processes with Finitely Many States

Ronald Pyke

#### Abstract

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.

#### Article information

Source
Ann. Math. Statist. Volume 32, Number 4 (1961), 1243-1259.

Dates
First available in Project Euclid: 27 April 2007

http://projecteuclid.org/euclid.aoms/1177704864

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