Probability density of the empirical wavelet coefficients of a noisy chaos - Université Paris 1 Panthéon-Sorbonne Accéder directement au contenu
Article Dans Une Revue Physica D: Nonlinear Phenomena Année : 2014

Probability density of the empirical wavelet coefficients of a noisy chaos

Résumé

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.
Fichier non déposé

Dates et versions

hal-01310473 , version 1 (02-05-2016)

Identifiants

Citer

Matthieu Garcin, Dominique Guegan. Probability density of the empirical wavelet coefficients of a noisy chaos. Physica D: Nonlinear Phenomena, 2014, 276, pp.28-47. ⟨10.1016/j.physd.2014.03.005⟩. ⟨hal-01310473⟩
71 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More