The present paper is concerned with the estimation of the transition distributions of a Markov
renewal process with finitely many states. A natural estimator of the transition distributions is …

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 …

This paper contains the definition of and some preliminary results on Markov Renewal
processes and Semi-Markov processes. The close relationship between these two types of …

In ordinary renewal theory, the asymptotic values of the mean and variance of the number of
renewals are obtained in terms of the moments of the distribution of the time interval …

For us a semi-Markov process is a separable process {X,, t! O} witli denumerable state space
I such that if {t if XS= Xt for all 0< s_< Yt= t-sup [s: O? s< t, X_ XJ] otherwise, then the two …

Very simple renewal theory concepts are used to calculate transition probabilities, and their
limits, for a Markov process subjected to an independent Poisson process of killing events …

The principal results of Resnick and Neuts (1970) and Resnick (1971) concerning limiting
distributions for the maxima of a sequence of random variables defined on a Markov chain …

The problem considered is that of estimating the limit probability distribution (equilibrium
distribution) πof a denumerable continuous time Markov process using only the matrix Q of …

We are interested in some limiting distributions of MRP N (t)={N j (t), 1≤ j≤ r} or the total
sojourn times in each state for a special MRP, in which transition distribution functions have …

1. Introduction. A Markov renewal process [7, 8],[Ni (t), N2 (t),*., NR (t)] is an extension of an
ordinary renewal process having considerable practical importance. Whereas the ordinary …