On the truncated Hausdorff moment problem under Sobolev regularity conditions

Abstract

We study the problem of approximating the recovery of a probability distribution on the unit interval from its first k moments. As main result we obtain an upper bound on the L1 reconstruction error under the regularity assumption that the log-density function has square-integrable derivatives up to some natural order r>1. Our bound is of order O(k−r). A comparative study relates our findings to alternative conditions on the distributions.