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

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

doi:10.1016/j.acha.2011.04.003

Journal articles

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

Marianne Clausel ¹ François Roueff ² Murad S. Taqqu ³ Ciprian A. Tudor ⁴

1 SAM - Statistique Apprentissage Machine

LJK - Laboratoire Jean Kuntzmann

2 LTCI - Laboratoire Traitement et Communication de l'Information

3 BU - Boston University [Boston]

4 LPP - Laboratoire Paul Painlevé - UMR 8524

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 : Long--range dependence Hermite processes Wavelet coefficients Wiener chaos self-similar processes Long--range dependence.

Document type :

Journal articles

Domain :

Mathematics [math] / Probability [math.PR]

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Submitted on : Friday, June 11, 2010 - 10:15:13 AM
Last modification on : Wednesday, March 23, 2022 - 3:50:06 PM
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Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory

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

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