Entropy and the discrete central limit theorem

被引：3

作者：

Gavalakis, Lampros ^{[1
]}

Kontoyiannis, Ioannis ^{[2
]}

机构：

[1] Univ Cambridge, Dept Engn, Trumpington St, Cambridge CB2 1PZ, England

[2] Univ Cambridge, Ctr Math Sci, DPMMS, Stat Lab, Wilberforce Rd, Cambridge CB3 0WB, England

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：

Central limit theorem; Entropy; Fisher information; Relative entropy; Bernoulli part decomposition; Lattice distribution; Convolution inequality; MONOTONICITY; INFORMATION; INEQUALITY;

D O I：

10.1016/j.spa.2023.104294

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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 -> infinity.

引用

页数：10

共 33 条

[1]

[Anonymous], 1950, An Introduction to Probability Theory and Its Applications

[2] Solution of Shannon's problem on the monotonicity of entropy [J].