度量半群中的hoffmann-jorgensen不等式

IF 2.1 1区数学 Q1 STATISTICS & PROBABILITY Annals of Probability Pub Date : 2016-10-07 DOI:10.1214/16-AOP1160

A. Khare, B. Rajaratnam

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引用次数: 10

摘要

我们证明了Hoffmann-Jorgensen对不等式的改进，这有三个重要的原因。首先，即使对于实值随机变量，我们的结果也比最先进的结果有所改进。其次，该结果统一了巴拿赫空间文献中的几个版本，包括Johnson和Schechtman Ann的版本。[p] . 17(1989) 789-808。[约28 (2000)851-862]，Hitczenko和Montgomery-Smith Ann。约29(2001)447-466]。最后，我们证明了Hoffmann-Jorgensen不等式(包括我们的推广版本)不仅在Banach空间中成立，而且更普遍地在一个非常原始的数学框架中成立:一个度量半群g。这包括赋范线性空间以及所有紧的、离散的或(连通的)阿贝尔李群。

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THE HOFFMANN-JORGENSEN INEQUALITY IN METRIC SEMIGROUPS

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.

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来源期刊

Annals of Probability 数学-统计学与概率论

CiteScore

4.60

自引率

8.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Annals of Probability publishes research papers in modern probability theory, its relations to other areas of mathematics, and its applications in the physical and biological sciences. Emphasis is on importance, interest, and originality – formal novelty and correctness are not sufficient for publication. The Annals will also publish authoritative review papers and surveys of areas in vigorous development.

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