Superposed continuous renewal processes: A Markov renewal approach
type: Item
instance of: scholarly article
title: Superposed continuous renewal processes: A Markov renewal approach
zbMATH Open document ID: 0852.60095
DOI: 10.1016/0304-4149(95)00079-8
author: Gerold Alsmeyer
published in: Stochastic Processes and their Applications
publication date: 1996-08-05T00:00:00Z
review text: Let \((S_n)_{n \geq 1}\) be the point process obtained as superposition of \(p \geq 2\) independent renewal processes. Though in general this process is no longer a renewal process, it shares the asymptotic properties of renewal processes as given in the renewal theorems. This has been shown by \textit{C. Y. T. Lam} and \textit{J. P. Lehoczky} [Adv. Appl. Probab. 23, No. 1, 64-85 (1991; Zbl 0723.60109)]. The author describes the superposition as a Markov renewal process and applies the Markov renewal theorems. This approach simplifies proofs and allows remarkable extensions. He states the generalized versions of the classical renewal theorems and, in case the increments of the basic renewal processes have spread out distributions, results on rates of convergence. As a prerequisite he proves a Stone-type decomposition for the Markov renewal measure of the superposition and uses the coupling technique.
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60K15
zbMATH DE Number: 894802
zbMATH Keywords: superpositions
zbMATH Keywords: Markov renewal equation
zbMATH Keywords: Markov renewal theorem
zbMATH Keywords: Stone-type decomposition
zbMATH Keywords: coupling
reviewed by: Helmut Wegmann
MaRDI profile type: Publication
full work available at URL: 0304-4149(95)00079-8
OpenAlex ID: W2008826821
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description: scientific article; zbMATH DE number 894802