The Hausdorff moment problem under finite additivity

Enrique Miranda, Gert de Cooman, Erik Quaeghebeur

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)

Abstract

We investigate to what extent finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.

Original languageEnglish
Pages (from-to)663-693
Number of pages31
JournalJournal of Theoretical Probability
Volume20
Issue number3
DOIs
Publication statusPublished - Sep 2007
Externally publishedYes

Keywords

  • Coherent lower prevision
  • Complete monotonicity
  • Hausdorff moment problem
  • Lower distribution function

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