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.
Publié le : 1994-10-14
Classification:
Decoupling principle,
symmetric tensor products,
random polynomials,
multiple random series,
multiple stochastic integrals,
random multilinear forms,
random chaos,
tail inequalities,
polarization,
symmetrization,
Banach space,
rearrangement invariant,
Orlicz space,
Loretz space,
Rademacher sequence,
$U$-statistcs,
60B11,
46M05,
60H07,
46E30,
60E15,
62H05,
62G30
@article{1176988481,
author = {de la Pena, V. H. and Montgomery-Smith, S. J. and Szulga, Jerzy},
title = {Contraction and Decoupling Inequalities for Multilinear Forms and $U$-Statistics},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 1745-1765},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988481}
}
de la Pena, V. H.; Montgomery-Smith, S. J.; Szulga, Jerzy. Contraction and Decoupling Inequalities for Multilinear Forms and $U$-Statistics. Ann. Probab., Tome 22 (1994) no. 4, pp. 1745-1765. http://gdmltest.u-ga.fr/item/1176988481/