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THE HOFFMANN-JORGENSEN INEQUALITY IN METRIC SEMIGROUPS

Khare, Apoorva and Rajaratnam, Bala (2017) THE HOFFMANN-JORGENSEN INEQUALITY IN METRIC SEMIGROUPS. In: ANNALS OF PROBABILITY, 45 (6). pp. 4101-4111.

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Official URL: http://dx.doi.org/10.1214/16-AOP1160

Abstract

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.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the INST MATHEMATICAL STATISTICS, 3163 SOMERSET DR, CLEVELAND, OH 44122 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 27 Dec 2017 10:11
Last Modified: 27 Dec 2017 10:11
URI: http://eprints.iisc.ac.in/id/eprint/58551

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