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
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 BU - Boston University [Boston]
4 LPP - Laboratoire Paul Painlevé - UMR 8524

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.

Domains: Probability [math.PR]

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