  Random Wavelet Series form a class of random processes with multifractal
properties. We give three applications of this construction. First, we
synthesize a random function having any given spectrum of singularities
satisfying some conditions (but including non-concave spectra). Second, these
processes provide examples where the multifractal spectrum coincides with the
spectrum of large deviations, and we show how to recover it numerically.
Finally, particular cases of these processes satisfy a generalized
selfsimilarity relation proposed in the theory of fully developed turbulence.
