## Real Analysis Exchange

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

### Maximum entropy and moment problems.

#### 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