Probability density of the wavelet coefficients of a noisy chaos.

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.