WAVELET ANALYSIS OF FRACTAL DISTRIBUTION

Using the continuous wavelet transform, rye define a new formalism tha t provides a statistical description of the singularities of a fractal distribution. This wavelet based method is a generalization of the cl assical multifractal formalism developed for characterizing singular m easures. Our purpose is illustrated on pedagogical examples including Brownian functions. For a particular class of fractal distributions, o ur heuristic considerations can be established in a rigourous way.