Probability density of the wavelet coefficients of a noisy chaos

Matthieu Garcin () and Dominique Guegan ()
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Matthieu Garcin: Centre d'Economie de la Sorbonne et Natixis Asset Management, https://centredeconomiesorbonne.cnrs.fr
Dominique Guegan: Centre d'Economie de la Sorbonne, https://cv.archives-ouvertes.fr/dominique-guegan

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

Abstract: We are interested in the random wavelet coefficients of a noisy signal when this signal is the unidimensional or multidimensional attractor of a chaos. More precisely we give an expression for the probability density of such coefficients. If the noise is a dynamic noise, then our expression is exact. If we face a measurement noise, then we propose two approximations using Taylor expansion or Edgeworth expansion. We give some illustrations of these theoretical results for the logistic map, the tent map and the Hénon map, perturbed by a Gaussian or a Cauchy noise

Keywords: Wavelets; dynamical systems; chaos; noise; alpha-stable (search for similar items in EconPapers)
Pages: 29 pages
Date: 2013-01
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Working Paper: Probability density of the wavelet coefficients of a noisy chaos (2013)
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