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October, 1994 Contraction and Decoupling Inequalities for Multilinear Forms and $U$-Statistics
V. H. de la Pena, S. J. Montgomery-Smith, Jerzy Szulga
Ann. Probab. 22(4): 1745-1765 (October, 1994). DOI: 10.1214/aop/1176988481

Abstract

We prove decoupling inequalities for random polynomials in independent random variables with coefficients in vector space. We use various means of comparison, including rearrangement invariant norms (e.g., Orlicz and Lorentz norms), tail distributions, tightness, hypercontractivity and so forth.

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V. H. de la Pena. S. J. Montgomery-Smith. Jerzy Szulga. "Contraction and Decoupling Inequalities for Multilinear Forms and $U$-Statistics." Ann. Probab. 22 (4) 1745 - 1765, October, 1994. https://doi.org/10.1214/aop/1176988481

Information

Published: October, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0861.60008
MathSciNet: MR1331202
Digital Object Identifier: 10.1214/aop/1176988481

Subjects:
Primary: 60B11
Secondary: 46E30 , 46M05 , 60E15 , 60H07 , 62G30 , 62H05

Keywords: $U$-statistcs , Banach space , Decoupling principle , Loretz space , multiple random series , multiple stochastic integrals , Orlicz space , polarization , Rademacher sequence , random chaos , random multilinear forms , random polynomials , rearrangement invariant , symmetric tensor products , symmetrization , tail inequalities

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 4 • October, 1994
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