Entropy and the discrete central limit theorem

被引：0

作者：

Gavalakis, Lampros ^{[1
]}

Kontoyiannis, Ioannis ^{[2
]}

机构：

[1] Department of Engineering, University of Cambridge, Trumpington Street, Cambridge,CB2 1PZ, United Kingdom

[2] Statistical Laboratory, DPMMS, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge,CB3 0WB, United Kingdom

来源：

Stochastic Processes and their Applications | 2024年 / 170卷

基金：

英国工程与自然科学研究理事会;

关键词：

Fisher information matrix - Information theory - Random variables;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of n independent and identically distributed lattice random variables and an appropriately discretised Gaussian, vanishes as n→∞. © 2024 Elsevier B.V.

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