Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory

Marianne Clausel; François Roueff; Murad S. Taqqu; Ciprian Tudor

doi:10.1016/j.acha.2011.04.003

Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory

Marianne Clausel
, François Roueff
, Murad S. Taqqu
, Ciprian Tudor

Université Gustave Eiffel
CNRS LTCI
Boston University
CNRS UMR 8524

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

9 Citations (Scopus)

Résumé

We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non-linear filter with Gaussian input. The wavelet coefficients that appear in the limit are random, typically non-Gaussian and belong to a Wiener chaos. They can be interpreted as wavelet coefficients of a generalized self-similar process.

langue originale	Anglais
Pages (de - à)	223-241
Nombre de pages	19
journal	Applied and Computational Harmonic Analysis
Volume	32
Numéro de publication	2
Les DOIs	https://doi.org/10.1016/j.acha.2011.04.003
état	Publié - 1 mars 2012
Modification externe	Oui

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10.1016/j.acha.2011.04.003

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abstract = "We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non-linear filter with Gaussian input. The wavelet coefficients that appear in the limit are random, typically non-Gaussian and belong to a Wiener chaos. They can be interpreted as wavelet coefficients of a generalized self-similar process.",

keywords = "Hermite processes, Long-range dependence, Self-similar processes, Wavelet coefficients, Wiener chaos",

author = "Marianne Clausel and Fran{\c c}ois Roueff and Taqqu, \{Murad S.\} and Ciprian Tudor",

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AU - Roueff, François

AU - Taqqu, Murad S.

AU - Tudor, Ciprian

PY - 2012/3/1

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N2 - We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non-linear filter with Gaussian input. The wavelet coefficients that appear in the limit are random, typically non-Gaussian and belong to a Wiener chaos. They can be interpreted as wavelet coefficients of a generalized self-similar process.

AB - We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non-linear filter with Gaussian input. The wavelet coefficients that appear in the limit are random, typically non-Gaussian and belong to a Wiener chaos. They can be interpreted as wavelet coefficients of a generalized self-similar process.

KW - Hermite processes

KW - Long-range dependence

KW - Self-similar processes

KW - Wavelet coefficients

KW - Wiener chaos

U2 - 10.1016/j.acha.2011.04.003

DO - 10.1016/j.acha.2011.04.003

M3 - Article

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SN - 1063-5203

VL - 32

SP - 223

EP - 241

JO - Applied and Computational Harmonic Analysis

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Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory

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