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Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory |
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| Authors: | Marianne Clausel François Roueff Murad S. Taqqu Ciprian Tudor |
| Affiliation: | 1. Laboratoire d?Analyse et de Mathématiques Appliquées, UMR 8050 du CNRS, Université Paris Est, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France;2. Institut Telecom, Telecom Paris, CNRS LTCI, 46 rue Barrault, 75634 Paris Cedex 13, France;3. Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA;4. Laboratoire Paul Painlevé, UMR 8524 du CNRS, Université Lille 1, 59655 Villeneuve d?Ascq, France |
| 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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