Entropy-convergence in Stieltjes and Hamburger moment problem
type: Item
instance of: scholarly article
title: Entropy-convergence in Stieltjes and Hamburger moment problem
zbMATH Open document ID: 0909.44003
DOI: 10.1016/S0096-3003(96)00305-0
author: M. Frontini
author: Aldo Tagliani
published in: Applied Mathematics and Computation
publication date: 1999-04-07T00:00:00Z
review text: Let \(\{\mu_n\}^\infty_0\) be a sequence of moments for the Hamburger moment problem and let \(f(x)\) be the (unknown) density function: \(\mu_n= \int_\mathbb{R} x^n f(x)dx\), \(n=0,1, \dots\) The maximal entropy principle is a formal procedure for obtaining approximants \(f_M\) of \(f\) with first \(M+1\) moments \(\{\mu_j \}^M_0\) equal to the given ones. It is shown that if the moment sequence uniquely determines the density function, then \(\lim_{M \to \infty} H[f_M] =H[f]\), where \(H[f]=-\int_\mathbb{R} f(x)\ln f(x) dx\) is the Boltzmann-Shannon entropy. The same result is obtained for the Stieltjes moment problem. In a previous publication the authors considered the case of finite moment sequences [J. Math. Phys. 35, No. 12, 6748-6756 (1994; Zbl 0830.41020)].
reviewed by: Khristo N. Boyadzhiev
Mathematics Subject Classification ID: 44A60
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 28D20
zbMATH DE Number: 1183162
zbMATH Keywords: entropy-convergence
zbMATH Keywords: Hamburger moment problem
zbMATH Keywords: maximal entropy principle
zbMATH Keywords: Boltzmann-Shannon entropy
zbMATH Keywords: Stieltjes moment problem
MaRDI profile type: Publication
cites work: I-divergence geometry of probability distributions and minimization problems
cites work: Maximum entropy in the finite Stieltjes and Hamburger moment problem
cites work: Convergence of Best Entropy Estimates
cites work: Q3849152
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full work available at URL: s0096-3003(96)00305-0
OpenAlex ID: W2042105895
description: scientific article; zbMATH DE number 1183162