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

Marianne Clausel 1 François Roueff 2 Murad Taqqu 3 Ciprian 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.
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Marianne Clausel, François Roueff, Murad Taqqu, Ciprian Tudor. Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory. Applied and Computational Harmonic Analysis, Elsevier, 2012, 32 (2), pp.223-241. ⟨10.1016/j.acha.2011.04.003⟩. ⟨hal-00491303⟩

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