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October 2002 Orlicz norms of sequences of random variables
Yehoram Gordon, Alexander Litvak, Carsten Schütt, Elisabeth Werner
Ann. Probab. 30(4): 1833-1853 (October 2002). DOI: 10.1214/aop/1039548373

Abstract

Let $f_{i}$, $i=1,\dots,n$, be copies of a random variable f and let N be an Orlicz function. We show that for every $x\in \mathbb{R}^{n}$ the expectation $\mathbf{E} \| (x_i f_i) _{i=1}^n \|_N $ is maximal (up to an absolute constant) if $f _{i}$, $i=1,\dots,n$, are independent. In that case we show that the expectation $\mathbf{E} \| (x_i f_i) _{i=1}^n \| _N $ is equivalent to $\|x\| _M$, for some Orlicz function M depending on N and on distribution of f only. We provide applications of this result.

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Yehoram Gordon. Alexander Litvak. Carsten Schütt. Elisabeth Werner. "Orlicz norms of sequences of random variables." Ann. Probab. 30 (4) 1833 - 1853, October 2002. https://doi.org/10.1214/aop/1039548373

Information

Published: October 2002
First available in Project Euclid: 10 December 2002

zbMATH: 1016.60008
MathSciNet: MR1944007
Digital Object Identifier: 10.1214/aop/1039548373

Subjects:
Primary: 46B07 , 46B09 , 46B45 , 60B99 , 60G50 , 60G51

Keywords: Orlicz norms , random variables

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.30 • No. 4 • October 2002
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