Proceedings of the Centre for Mathematics and its Applications

The convergence of entropic estimates for moment problems

A. S. Lewis

Full-text: Open access

Abstract

We show that if $x_n$ is optimal for the problem \[ sup\left\{\sum_{x_n}{1} log x(s)ds | \sum_0^1 (x(s)- \hat{x}(s))s^i ds = 0 , i = 0, \cdots,n , 0 \leq x \in L_1[0,1]\right\}, \] then $\frac{1}{x_n} \rightarrow \frac{1}{\hat{x}}$ weakly in $L_1$ (providing $\hat{x}$ is continuous and strictly positive). This result is a special case of a theorem for more general entropic objectives and underlying spaces.

Article information

Source
Workshop/Miniconference on Functional Analysis and Optimization. Simon Fitzpatrick and John Giles, eds. Proceedings of the Centre for Mathematical Analysis, v. 20. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1988), 100-115

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416340107

Mathematical Reviews number (MathSciNet)
MR1009598

Zentralblatt MATH identifier
0673.41021

Citation

Lewis, A. S. The convergence of entropic estimates for moment problems. Workshop/Miniconference on Functional Analysis and Optimization, 100--115, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1988. https://projecteuclid.org/euclid.pcma/1416340107


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