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Wavelet analysis of multifractal functions

Multifractal signals are characterized by a local Holder exponent that may change completely from point to point. We show that wavelet methods are an extremely efficient tool for determining the exact Holder exponent of a function, or at least, for getting some information about this Holder exponent, such as the Spectrum of Singularities. We construct functions that have a given Holder exponent in a deterministic setting and also in a probabilistic setting (we then obtain the Multifractional Brownian Motion); we also study the Multifractal Formalism for Functions and give some results about its validity.