Wavelet series built using multifractal measures

Let mu be a positive locally finite Borel measure on R. A natural way to construct multifractal wavelet series F-mu (x) = Sigma(j >= 0),(k is an element of Z)d(j),(k)psi(j),(k)(x) is to set vertical bar d(j,k)vertical bar = 2(-j(s0-1/p0))mu([k2(-j), (k+1))(1/p0) where s0, p0 >= 0, so - 1/po > 0. Under suitable conditions, the function FP inherits the multifractal properties of mu. The transposition of multifractal properties works with most classes of statistically self-similar multifractal measures. Several perturbations of the wavelet coefficients and their impact on the multifractal nature of FP are studied. As an application, the multifractal spectrum of the celebrated W-cascades introduced by Arneodo et al. is obtained.