Real Analysis Exchange

Maximum entropy and moment problems.

C.-G. Ambrozie

Full-text: Open access

Abstract

We study moment problems in which one searches for a probability density on ${\R}^n$ by using insufficient information given in an integral form. We characterize the existence of the representing densities for a finite multi--sequence of moments by the solvability of a concrete finite system of equations. Its solution provides the (unique) representing density of maximum entropy allowed by the given data, that turns out to be the exponential of a polynomial to be determined. For all densities of this form, the system to be solved can be taken linear to be provided sufficiently many moments are known.

Article information

Source
Real Anal. Exchange, Volume 29, Number 2 (2003), 607-629.

Dates
First available in Project Euclid: 7 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149698552

Mathematical Reviews number (MathSciNet)
MR2083800

Zentralblatt MATH identifier
1083.44501

Subjects
Primary: 44A60: Moment problems 49J99: None of the above, but in this section

Keywords
moment problem representing measure entropy

Citation

Ambrozie, C.-G. Maximum entropy and moment problems. Real Anal. Exchange 29 (2003), no. 2, 607--629. https://projecteuclid.org/euclid.rae/1149698552


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