Stochastic expansions in an overcomplete wavelet dictionary

We consider random functions defined in terms of members of an overcomplete wavelet dictionary. The function is modelled as a sum of wavelet component s at arbitrary positions and scales where the locations of the wavelet comp onents and the magnitudes of their coefficients are chosen with respect to a marked Poisson process model. The relationships between the parameters of the model and the parameters of those Besov spaces within which realizatio ns will fall are investigated. The models allow functions with specified re gularity properties to be generated. They can potentially be used as priors in a Bayesian approach to curve estimation, extending current standard wav elet methods to be free from the dyadic positions and scales of the basis f unctions.