CONCENTRATION OF THE INFORMATION IN DATA WITH LOG-CONCAVE DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Bobkov, Sergey; Madiman, Mokshay
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Yale University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP592
• 发表日期: 2011
• 页码: 1528-1543
• 关键词: mcmillan-breiman theorem; ergodic theorem; SPACES; PROOF

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.