UPCROSSING INEQUALITIES FOR STATIONARY SEQUENCES AND APPLICATIONS

• 成果类型: Article
• 署名作者: Hochman, Michael
• 署名单位: Hebrew University of Jerusalem
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP460
• 发表日期: 2009
• 页码: 2135-2149
• 关键词: averages

摘要

For arrays (S(i, j))(1 <= i <= j) of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process (S(l, n))(n=1)(infinity) can be bounded in terms of a measure of the mean subadditivity of the process (S(i, j))(1 <= i <= j). We derive universal upcrossing inequalities with exponential decay for Kingman's subadditive ergodic theorem, the Shannon-MacMillan-Breiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.