The point process approach for fractionally differentiated random walks under heavy traffic
type: Item
instance of: scholarly article
title: The point process approach for fractionally differentiated random walks under heavy traffic
zbMATH Open document ID: 1264.60026
published in: Stochastic Processes and their Applications
publication date: 2012-10-26T00:00:00Z
review text: Let \((X_i)_{i \geq 1}\) be a sequence of independent random variables, having common distribution function \(F\) which is centered and belongs to the domain of attraction of a stable law with index \(\alpha\), in \((1,2)\). Let \(S_n = \sum_{0\leq i < n} g_i X_{n-i}\), where \(g(x) = \sum_{i \geq 0}g_i x^i\) is a power series with radius of convergence \(1\). A heavy traffic approximation describes the limiting behaviour of some functional of the process \((S_n)\). In this paper, the authors prove a point process form of a heavy traffic approximation for the supremum functional. In the sequel, a maximal-type inequality is proved for the process.
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 60G22
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 62P20
zbMATH DE Number: 6099217
zbMATH Keywords: heavy traffic
zbMATH Keywords: point process
zbMATH Keywords: fractional random walk
zbMATH Keywords: FARIMA process
zbMATH Keywords: Poisson process
author: Philippe Barbe
author: W. P. McCormick
reviewed by: Sreenivasan Ravi
MaRDI profile type: Publication
full work available at URL: j.spa.2012.08.008
OpenAlex ID: W2007797897
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DOI: 10.1016/J.SPA.2012.08.008
description: scientific article; zbMATH DE number 6099217