On the truncated Hausdorff moment problem under Sobolev regularity conditions

W. Zellinger, B. Moser. On the truncated Hausdorff moment problem under Sobolev regularity conditions. Applied Mathematics and Computation, volume 400, pages 126057, DOI 10.1016/j.amc.2021.126057, 7, 2021.

Autoren
  • Werner Zellinger
  • Bernhard A. Moser
TypArtikel
JournalApplied Mathematics and Computation
VerlagElsevier
Band400
DOI10.1016/j.amc.2021.126057
Monat7
Jahr2021
Seiten126057
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.