Estimation of the Memory Parameter of the Infinite Source Poisson Process

Fay, Gilles; Roueff, François; Soulier, Philippe

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.3150/07-BEJ5123

URL permanente :

http://hdl.handle.net/20.500.12210/123142

Titre :

Estimation of the Memory Parameter of the Infinite Source Poisson Process

Auteur(s) :

Fay, Gilles [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Roueff, François [Auteur]
Laboratoire Traitement et Communication de l'Information [LTCI]
Soulier, Philippe [Auteur]
Modélisation aléatoire de Paris X [MODAL'X]

Titre de la revue :

Bernoulli

Pagination :

473--491

Éditeur :

Bernoulli Society for Mathematical Statistics and Probability

Date de publication :

2007

ISSN :

1350-7265

Discipline(s) HAL :

Mathématiques [math]/Statistiques [math.ST]

Résumé en anglais : [en]

Long-range dependence induced by heavy tails is a widely reported feature of internet traffic. Long-range dependence can be defined as the regular variation of the variance of the integrated process, and half the index of ...
Lire la suite >Long-range dependence induced by heavy tails is a widely reported feature of internet traffic. Long-range dependence can be defined as the regular variation of the variance of the integrated process, and half the index of regular variation is then referred to as the Hurst index. The infinite-source Poisson process (a particular case of which is the $M/G/\infty$ queue) is a simple and popular model with this property, when the tail of the service time distribution is regularly varying. The Hurst index of the infinite-source Poisson process is then related to the index of regular variation of the service times. In this paper, we present a wavelet-based estimator of the Hurst index of this process, when it is observed either continuously or discretely over an increasing time interval. Our estimator is shown to be consistent and robust to some form of non-stationarity. Its rate of convergence is investigated.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Commentaire :

Final version

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T17:36:18Z

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