The limit of a renewal reward process with heavy-tailed rewards is not a linear fractional stable motion
type: Item
instance of: scholarly article
title: The limit of a renewal reward process with heavy-tailed rewards is not a linear fractional stable motion
zbMATH Open document ID: 0963.60032
DOI: 10.2307/3318508
author: Vladas Pipiras
author: Murad S. Taqqu
published in: Bernoulli
publication date: 2001-06-13T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bj/1081449595
review text: There are considered a renewal reward process with both inter-renewal times and rewards that have heavy tails of exponents \(\alpha\) and \(\beta\), respectively, where \(1< \alpha< 2\), \(0<\beta<2\). It was proved by \textit{J. B. Levy} and \textit{M. S. Taqqu} [ibid. 6, No. 1, 23-44 (2000; Zbl 0954.60071)] that the suitably normalized renewal reward process converges to Lévy stable motion with index \(\beta\), possesses stationary increments and is self-similar in the case \(\beta>\alpha\). The limit process was identified through its finite-dimensional characteristic functions. The authors provide an integral representation for the process and show that it does not belong to the family of linear fractional stable motions.
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60K05
zbMATH DE Number: 1529276
zbMATH Keywords: stable distributions
zbMATH Keywords: self-similar processes
zbMATH Keywords: renewal reward processes
zbMATH Keywords: stationary increments
reviewed by: Valentin Topchii
MaRDI profile type: Publication
OpenAlex ID: W2000459950
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description: scientific article; zbMATH DE number 1529276