Titre :

High order chaotic limits of wavelet scalograms under long--range dependence

Auteur(s) :

Clausel, Marianne [Auteur]
Statistique Apprentissage Machine [SAM]
Roueff, François [Auteur]
Laboratoire Traitement et Communication de l'Information [LTCI]
Taqqu, Murad [Auteur]
Department of Mathematics and Statistics [Boston]
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

ALEA : Latin American Journal of Probability and Mathematical Statistics

Pagination :

979­-1011

Éditeur :

Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....]

Date de publication :

2013-12-31

ISSN :

1980-0436

Mot(s)-clé(s) en anglais :

Wiener chaos
Long--range dependence
Hermite processes
Wavelet coefficients
self-similar processes
Long--range dependence.

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Théorie [stat.TH]

Résumé en anglais : [en]

Let $G$ be a non--linear function of a Gaussian process $\{X_t\}_{t\in\mathbb{Z}}$ with long--range dependence. The resulting process $\{G(X_t)\}_{t\in\mathbb{Z}}$ is not Gaussian when $G$ is not linear. We consider random ...
Lire la suite >Let $G$ be a non--linear function of a Gaussian process $\{X_t\}_{t\in\mathbb{Z}}$ with long--range dependence. The resulting process $\{G(X_t)\}_{t\in\mathbb{Z}}$ is not Gaussian when $G$ is not linear. We consider random wavelet coefficients associated with $\{G(X_t)\}_{t\in\mathbb{Z}}$ and the corresponding wavelet scalogram which is the average of squares of wavelet coefficients over locations. We obtain the asymptotic behavior of the scalogram as the number of observations and scales tend to infinity. It is known that when $G$ is a Hermite polynomial of any order, then the limit is either the Gaussian or the Rosenblatt distribution, that is, the limit can be represented by a multiple Wiener-Itô integral of order one or two. We show, however, that there are large classes of functions $G$ which yield a higher order Hermite distribution, that is, the limit can be represented by a a multiple Wiener-Itô integral of order greater than two.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL