Titre :

A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter

Auteur(s) :

Bardet, Jean-Marc [Auteur]
Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) [SAMM]
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) [SAMM]

Titre de la revue :

Stochastic Analysis and Applications

Pagination :

2331-2362

Éditeur :

Taylor & Francis: STM, Behavioural Science and Public Health Titles

Date de publication :

2010

ISSN :

0736-2994

Mot(s)-clé(s) en anglais :

Multiple Wiener-Itô integral
wavelet analysis
Rosenblatt process
fractional Brownian motion
noncentral limit theorem
self-similarity
parameter estimation

Discipline(s) HAL :

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

Résumé en anglais : [en]

By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior ...
Lire la suite >By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T10:57:18Z