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2003-2004 Maximum entropy and moment problems.
C.-G. Ambrozie
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Real Anal. Exchange 29(2): 607-629 (2003-2004).


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.


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C.-G. Ambrozie. "Maximum entropy and moment problems.." Real Anal. Exchange 29 (2) 607 - 629, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 7 June 2006

zbMATH: 1083.44501
MathSciNet: MR2083800

Primary: 44A60 , 49J99

Keywords: Entropy , Moment problem , representing measure

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 2 • 2003-2004
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