Title :

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

Author(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]

Journal title :

Stochastic Analysis and Applications

Pages :

2331-2362

Publisher :

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

Publication date :

2010

ISSN :

0736-2994

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T10:57:18Z