Probability density of the wavelet coefficients of a noisy chaos

Matthieu Garcin () and Dominique Guegan ()
Additional contact information
Matthieu Garcin: 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

Post-Print from HAL

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: noise; Wavelets; dynamical systems; Alpha-stable; Ondelettes; systèmes dynamiques; chaos; loi Alpha stable (search for similar items in EconPapers)
Date: 2013-01
New Economics Papers: this item is included in nep-ets
Note: View the original document on HAL open archive server: https://hal.science/hal-00800997
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in 2013

Downloads: (external link)
https://hal.science/hal-00800997/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00800997

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().