Decoupling inequalities for multilinear forms in independent symmetric random variables
type: Item
instance of: scholarly article
title: Decoupling inequalities for multilinear forms in independent symmetric random variables
zbMATH Open document ID: 0602.60025
author: Terry R. McConnell
author: Murad S. Taqqu
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: Let \(\tilde X=(\tilde X_ 1,\tilde X_ 2,...)\) be an independent copy of a sequence \(X=(X_ 1,X_ 2,...)\) of independent symmetric random variables. Let B be a symmetric bilinear form on \({\mathbb{R}}^{{\mathbb{N}}}\) whose matrix \(a=(a_{ij})\) with respect to the standard basis of \({\mathbb{R}}^{{\mathbb{N}}}\) satisfies \(a_{kk}=0\) for all k and \(a_{kj}=0\) for all but finitely many pairs (k,j). The aim of this paper is to establish the inequality \[ cE| B(X,X)|^ p\leq E| B(X,\tilde X)|^ p \] for \(1\leq p<\infty\).
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 11E76
zbMATH DE Number: 3971876
zbMATH Keywords: Khinchine's inequalities
zbMATH Keywords: random multilinear forms
zbMATH Keywords: convex functions
zbMATH Keywords: symmetric bilinear form
reviewed by: N. G. Gamkrelidze
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992449
OpenAlex ID: W2006375500
DOI: 10.1214/AOP/1176992449
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description: scientific article; zbMATH DE number 3971876