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Probability density of the wavelet coefficients of a noisy chaos

Author

Listed:
  • 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)

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.

Suggested Citation

  • Matthieu Garcin & Dominique Guegan, 2013. "Probability density of the wavelet coefficients of a noisy chaos," Post-Print hal-00800997, HAL.
    • Handle: RePEc:hal:journl:hal-00800997
    Note: View the original document on HAL open archive server: https://hal.science/hal-00800997
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    References listed on IDEAS

    as
    1. Matthieu Garcin & Dominique Guegan, 2012. "Extreme values of random or chaotic discretization steps," Documents de travail du Centre d'Economie de la Sorbonne 12033, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Dominique Guegan & Matthieu Garcin, 2012. "Extreme values of random or chaotic discretization steps and connected networks," Post-Print halshs-00750231, HAL.
    3. Dominique Guegan & Matthieu Garcin, 2012. "Extreme values of random or chaotic discretization steps and connected networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00750231, HAL.
    4. Matthieu Garcin & Dominique Guegan, 2012. "Extreme values of random or chaotic discretization steps," Post-Print hal-00706825, HAL.
    5. Blacher, René, 2003. "Multivariate quadratic forms of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 2-23, October.
    6. Dominique Guegan & Matthieu Garcin, 2012. "Extreme values of random or chaotic discretization steps and connected networks," PSE-Ecole d'économie de Paris (Postprint) halshs-00750231, HAL.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    noise; Wavelets; dynamical systems; Alpha-stable; Ondelettes; systèmes dynamiques; chaos; loi Alpha stable;
    All these keywords.

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