THE HOFFMANN-JORGENSEN INEQUALITY IN METRIC SEMIGROUPS

• 成果类型: Article
• 署名作者: Khare, Apoorva; Rajaratnam, Bala
• 署名单位: Stanford University; University of California System; University of California Davis; University of Sydney; Indian Institute of Science (IISC) - Bangalore
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1160
• 发表日期: 2017
• 页码: 4101-4111
• 关键词: independent random-variables; sums

摘要

We prove a refinement of the inequality by Hoffmann-Jorgensen that is significant for three reasons. First, our result improves on the state-of-the-art even for real-valued random variables. Second, the result unifies several versions in the Banach space literature, including those by Johnson and Schechtman [Ann. Probab. 17 (1989) 789-808], Klass and Nowicki [Ann. Probab. 28 (2000) 851-862], and Hitczenko and Montgomery-Smith [Ann. Probab. 29 (2001) 447-466]. Finally, we show that the Hoffmann-Jorgensen inequality (including our generalized version) holds not only in Banach spaces but more generally, in a very primitive mathematical framework required to state the inequality: a metric semigroup G. This includes normed linear spaces as well as all compact, discrete or (connected) abelian Lie groups.