Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards
type: Item
instance of: scholarly article
title: Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards
zbMATH Open document ID: 0954.60071
DOI: 10.2307/3318631
author: Joshua B. Levy
author: Murad S. Taqqu
published in: Bernoulli
publication date: 2001-02-11T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bj/1082665378
review text: This paper studies a superposition \(W^*\) of renewal-reward processes having inter-renewal time and reward distributions with heavy tails of exponents \(\alpha\) and \(\beta\), respectively, where \(1< \alpha< 2\), \(0<\beta<2\). In the case \(\beta\leq\alpha\), \(W^*\) suitably normalized converges to Lévy stable motion with index \(\beta\); see the authors [Ann. Sci. Math. Qué. 11, 95-110 (1987; Zbl 0646.60091)]. The present work re-iterates this result and establishes a limit for the case \(\beta>\alpha\), which is also a self-similar, symmetric \(\beta\)-stable process with stationary increments; here, however, the increments are dependent.
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60K30
zbMATH DE Number: 1428369
zbMATH Keywords: computer networks
zbMATH Keywords: infinite variance
zbMATH Keywords: self-similar processes
zbMATH Keywords: stable processes
zbMATH Keywords: telecommunications
MaRDI profile type: Publication
OpenAlex ID: W1974678258
description: scientific article; zbMATH DE number 1428369