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November 2012 Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails
Radosław Adamczak, Rafał Latała
Ann. Inst. H. Poincaré Probab. Statist. 48(4): 1103-1136 (November 2012). DOI: 10.1214/11-AIHP441

Abstract

We present two-sided estimates of moments and tails of polynomial chaoses of order at most three generated by independent symmetric random variables with log-concave tails as well as for chaoses of arbitrary order generated by independent symmetric exponential variables. The estimates involve only deterministic quantities and are optimal up to constants depending only on the order of the chaos variable.

Nous établissons un encadrement des moments et des queues d’un chaos polynomial d’ordre au plus trois engendré par des variables aléatoires indépendantes symétriques à queues log-concaves et pour des chaos d’ordre quelconque engendrés par des variables aléatoires indépendantes symétriques exponentielles. Ces estimations ne font intervenir que des quantités déterministes et sont optimales à des constantes près qui ne dépendent que de l’ordre du chaos.

Citation

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Radosław Adamczak. Rafał Latała. "Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails." Ann. Inst. H. Poincaré Probab. Statist. 48 (4) 1103 - 1136, November 2012. https://doi.org/10.1214/11-AIHP441

Information

Published: November 2012
First available in Project Euclid: 16 November 2012

zbMATH: 1263.60016
MathSciNet: MR3052405
Digital Object Identifier: 10.1214/11-AIHP441

Subjects:
Primary: Primary 60E15 , secondary 60G15

Keywords: Metric entropy , Polynomial chaoses , Tail and moment estimates

Rights: Copyright © 2012 Institut Henri Poincaré

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Vol.48 • No. 4 • November 2012
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