Recovering a probability density from a finite number of moments and local a priori information

The present paper deals with the reconstruction of an unknown probability density u in [0,1] from a finite number of moments and some additional local a priori information (location and type of sin gularities of u or du/dx). If the additional information may be represented by means of a density w, it is natural to select our estimator of u by minimizing some kind of discrepancy between u and we like euclidean distance or relative entropy. We compare the corresponding solutions in several numerical experiments.