Probability density of the empirical wavelet coefficients of a noisy chaos

Matthieu Garcin () and Dominique Guegan ()
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Matthieu Garcin: Natixis Asset Management - SAMS, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Dominique Guegan: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: We are interested in the random empirical wavelet coefficients of a noisy signal when this signal is a unidimensional or multidimensional chaos. More precisely we provide an expression of the conditional probability density of such coefficients, given a discrete observation grid. The noise is assumed to be described by a symmetric alpha-stable random variable. If the noise is a dynamic noise, then we present the exact expression of the probability density of each wavelet coefficient of the noisy signal. If we face a measurement noise, then the noise has a non-linear influence and we propose two approximations. The first one relies on a Taylor expansion whereas the second one, relying on an Edgeworth expansion, improves the first general Taylor approximation if the cumulants of the noise are defined. We give some illustrations of these theoretical results for the logistic map, the tent map and a multidimensional chaos, the Hénon map, disrupted by a Gaussian or a Cauchy noise.

Keywords: Wavelets; Dynamical systems; Chaos; Noise; Alpha-stable (search for similar items in EconPapers)
Date: 2014-05
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Citations: View citations in EconPapers (3)

Published in Physica D: Nonlinear Phenomena, 2014, 276, pp.28-47. ⟨10.1016/j.physd.2014.03.005⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-01310473

DOI: 10.1016/j.physd.2014.03.005

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