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

Radosław Adamczak; Rafał Latała

Annales de l'I.H.P. Probabilités et statistiques (2012)

  • Volume: 48, Issue: 4, page 1103-1136
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Adamczak, Radosław, and 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 48.4 (2012): 1103-1136. <http://eudml.org/doc/272075>.

@article{Adamczak2012,
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.},
author = {Adamczak, Radosław, Latała, Rafał},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {polynomial chaoses; tail and moment estimates; metric entropy},
language = {eng},
number = {4},
pages = {1103-1136},
publisher = {Gauthier-Villars},
title = {Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails},
url = {http://eudml.org/doc/272075},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Adamczak, Radosław
AU - Latała, Rafał
TI - Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 4
SP - 1103
EP - 1136
AB - 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.
LA - eng
KW - polynomial chaoses; tail and moment estimates; metric entropy
UR - http://eudml.org/doc/272075
ER -

References

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