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July, 1986 Decoupling Inequalities for Multilinear Forms in Independent Symmetric Random Variables
Terry R. McConnell, Murad S. Taqqu
Ann. Probab. 14(3): 943-954 (July, 1986). DOI: 10.1214/aop/1176992449


Let $X^1, X^2,\ldots$ be independent copies of a sequence $X = (X_1, X_2, \ldots)$ of independent symmetric random variables. Let $M$ be a symmetric multilinear form of rank $s$ on $\mathbb{R}^\mathbb{N}$ whose components $a_{i_1,\ldots, i_s}$ relative to the standard basis of $\mathbb{R}^\mathbb{N}$ satisfy $a_{i_1,\ldots, i_s} = 0$ for all but finitely many multi-indices and whenever two indices agree. If $\phi$ is nondecreasing, convex, $\phi(0) = 0$ and $\phi$ satisfies a $\Delta_2$ growth condition then $E\phi(|M(X,\ldots, X)|) \leq cE\phi(|M(X^1,\ldots, X^s)|),$ where $c$ depends only on $\phi$ and $s$.


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Terry R. McConnell. Murad S. Taqqu. "Decoupling Inequalities for Multilinear Forms in Independent Symmetric Random Variables." Ann. Probab. 14 (3) 943 - 954, July, 1986.


Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0602.60025
MathSciNet: MR841595
Digital Object Identifier: 10.1214/aop/1176992449

Primary: 60E15
Secondary: 10C10

Keywords: Convex functions , Khinchine's inequalities , random multilinear forms

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 3 • July, 1986
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