Statistical study of the wavelet analysis of fractional Brownian motion

Jean Marc Bardet

doi:10.1109/18.992817

Statistical study of the wavelet analysis of fractional Brownian motion

Jean Marc Bardet

Université de Toulouse

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

49 Citations (Scopus)

Résumé

We present a statistical study of wavelet coefficients of a fractional Brownian motion. A central limit theorem for empirical variances of exact wavelet coefficients is given. Under conditions on the mother wavelet and the choice of scales, a limit theorem is given for fitted wavelet coefficients computed from a time series. It provides an estimator for the self-similarity parameter of Gaussian time series.

langue originale	Anglais
Pages (de - à)	991-999
Nombre de pages	9
journal	IEEE Transactions on Information Theory
Volume	48
Numéro de publication	4
Les DOIs	https://doi.org/10.1109/18.992817
état	Publié - 1 avr. 2002
Modification externe	Oui

Accès au document

10.1109/18.992817

Contient cette citation

@article{f4b2b8394535485b919410b273dc6f0a,

title = "Statistical study of the wavelet analysis of fractional Brownian motion",

abstract = "We present a statistical study of wavelet coefficients of a fractional Brownian motion. A central limit theorem for empirical variances of exact wavelet coefficients is given. Under conditions on the mother wavelet and the choice of scales, a limit theorem is given for fitted wavelet coefficients computed from a time series. It provides an estimator for the self-similarity parameter of Gaussian time series.",

keywords = "Estimation of the self-similarity index, Fractional Brownian motion, Self-similarity, Wavelet analysis",

author = "Bardet, \{Jean Marc\}",

year = "2002",

month = apr,

day = "1",

doi = "10.1109/18.992817",

language = "English",

volume = "48",

pages = "991--999",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "4",

}

TY - JOUR

T1 - Statistical study of the wavelet analysis of fractional Brownian motion

AU - Bardet, Jean Marc

PY - 2002/4/1

Y1 - 2002/4/1

N2 - We present a statistical study of wavelet coefficients of a fractional Brownian motion. A central limit theorem for empirical variances of exact wavelet coefficients is given. Under conditions on the mother wavelet and the choice of scales, a limit theorem is given for fitted wavelet coefficients computed from a time series. It provides an estimator for the self-similarity parameter of Gaussian time series.

AB - We present a statistical study of wavelet coefficients of a fractional Brownian motion. A central limit theorem for empirical variances of exact wavelet coefficients is given. Under conditions on the mother wavelet and the choice of scales, a limit theorem is given for fitted wavelet coefficients computed from a time series. It provides an estimator for the self-similarity parameter of Gaussian time series.

KW - Estimation of the self-similarity index

KW - Fractional Brownian motion

KW - Self-similarity

KW - Wavelet analysis

U2 - 10.1109/18.992817

DO - 10.1109/18.992817

M3 - Article

AN - SCOPUS:0036539276

SN - 0018-9448

VL - 48

SP - 991

EP - 999

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 4

ER -

Statistical study of the wavelet analysis of fractional Brownian motion

Résumé

Accès au document

Empreinte digitale

Contient cette citation