Author:
Arjas Elja,Nummelin Esa,Tweedie Richard L.
Abstract
We show that if the increment distribution of a renewal process has some convolution non-singular with respect to Lebesgue measure, then the skeletons of the forward recurrence time process are φ-irreducible positive recurrent Markov chains. Known convergence properties of such chains give simple proofs of uniform versions of some old and new key renewal theorems; these show in particular that non-singularity assumptions on the increment and initial distributions enable the assumption of direct Riemann integrability to be dropped from the standard key renewal theorem. An application to Markov renewal processes is given.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference29 articles.
1. Arjas E. , Nummelin E. and Tweedie R. L. Semi-Markov processes on a general state space, a-theory and quasi-stationarity. Submitted for publication.
2. Measure Theory
3. Sur une classe de marches aléatoires;Bretagnolle;Ann. Inst. H. Poincaré,1967
4. Uniform rates of convergence for Markov chain transition probabilities
5. Periodicity in Markov renewal theory
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