Abstract
In [3], Kendall proved a solidarity theorem for irreducible denumerable discrete time Markov chains. Vere-Jones refined Kendall's theorem by obtaining uniform estimates [14], while Kingman proved analogous results for an irreducible continuous time Markov chain [4], [5].We derive similar solidarity theorems for an irreducible Markov renewal process. The transient case is discussed in Section 3, and Section 4 deals with the positive recurrent case. Recently Cheong also proved solidarity theorems for Semi-Markov processes [1]. His theorems use the Markovian structure, while our emphasis is on the renewal aspects of Markov renewal processes.An application to the M/G/1 queue is included in the last section.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference15 articles.
1. Teugels J. L. (1967) On the rate of convergence in renewal and Markov renewal processes. Purdue Univ. Dept. of Stat. Mimeo Series 107.
2. GEOMETRIC ERGODICITY IN DENUMERABLE MARKOV CHAINS
3. Limit Theorems for Markov Renewal Processes
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