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

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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.

Original language	English
Pages (from-to)	223-241
Number of pages	19
Journal	Applied and Computational Harmonic Analysis
Volume	32
Issue number	2
DOIs	https://doi.org/10.1016/j.acha.2011.04.003
Publication status	Published - 1 Mar 2012
Externally published	Yes

Keywords

Hermite processes
Long-range dependence
Self-similar processes
Wavelet coefficients
Wiener chaos

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10.1016/j.acha.2011.04.003

Cite this

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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.",

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

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AU - Clausel, Marianne

AU - Roueff, François

AU - Taqqu, Murad S.

AU - Tudor, Ciprian

PY - 2012/3/1

Y1 - 2012/3/1

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

AN - SCOPUS:84856470840

SN - 1063-5203

VL - 32

SP - 223

EP - 241

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

IS - 2

ER -

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

Abstract

Keywords

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