CONCENTRATION OF THE INFORMATION IN DATA WITH LOG-CONCAVE DISTRIBUTIONS

被引：55

作者：

Bobkov, Sergey ^{[1
]}

Madiman, Mokshay ^{[2
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Yale Univ, Dept Stat, New Haven, CT 06511 USA

来源：

ANNALS OF PROBABILITY | 2011年 / 39卷 / 04期

关键词：

Concentration; entropy; log-concave distributions; asymptotic equipartition property; Shannon-McMillan-Breiman theorem; MCMILLAN-BREIMAN THEOREM; ERGODIC THEOREM; SPACES; PROOF;

D O I：

10.1214/10-AOP592

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 concentration property of the functional - log f (X) is demonstrated, when a random vector X has a log-concave density f on R-n. This concentration property implies in particular an extension of the Shannon-McMillan-Breiman strong ergodic theorem to the class of discrete-time stochastic processes with log-concave marginals.

引用

页码：1528 / 1543

页数：16

共 21 条

[1] A SANDWICH PROOF OF THE SHANNON-MCMILLAN-BREIMAN THEOREM [J].