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.
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