Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails

Adamczak, Radosław; Latała, Rafał

doi:10.1214/11-AIHP441

Adamczak, Radosław ; Latała, Rafał

Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) no. 4, pp. 1103-1136.

Résumé
Abstract

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.

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.

MR Zbl | 1 citation dans Numdam

DOI : 10.1214/11-AIHP441

Classification : Primary 60E15, secondary, 60G15
Mots clés : polynomial chaoses, tail and moment estimates, metric entropy

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     title = {Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1103--1136},
     publisher = {Gauthier-Villars},
     volume = {48},
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     mrnumber = {3052405},
     zbl = {1263.60016},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1214/11-AIHP441/}
}

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Adamczak, Radosław; Latała, Rafał. Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails. Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) no. 4, pp. 1103-1136. doi : 10.1214/11-AIHP441. http://archive.numdam.org/articles/10.1214/11-AIHP441/

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