Moment and tail estimates for multidimensional chaoses generated by symmetric random variables with logarithmically concave tails

Rafał M. Łochowski. "Moment and tail estimates for multidimensional chaoses generated by symmetric random variables with logarithmically concave tails." Banach Center Publications 72.1 (2006): 161-176. <http://eudml.org/doc/282330>.

@article{RafałM2006,
abstract = {Two kinds of estimates are presented for tails and moments of random multidimensional chaoses $S = ∑ a_\{i₁,..., i_\{d\}\} X_\{i₁\}^\{(1)\} ⋯ X_\{i_\{d\}\}^\{(d)\}$ generated by symmetric random variables $X_\{i₁\}^\{(1)\},...,X_\{i_\{d\}\}^\{(d)\}$ with logarithmically concave tails. The estimates of the first kind are generalizations of bounds obtained by Arcones and Giné for Gaussian chaoses. They are exact up to constants depending only on the order d. Unfortunately, suprema of empirical processes are involved. The second kind estimates are based on comparison between moments of S and moments of some related Rademacher chaoses. The estimates for pth moment are exact up to a factor $(max(1,ln p))^\{d²\}$.},
author = {Rafał M. Łochowski},
journal = {Banach Center Publications},
keywords = {random chaos; moments},
language = {eng},
number = {1},
pages = {161-176},
title = {Moment and tail estimates for multidimensional chaoses generated by symmetric random variables with logarithmically concave tails},
url = {http://eudml.org/doc/282330},
volume = {72},
year = {2006},
}

TY - JOUR
AU - Rafał M. Łochowski
TI - Moment and tail estimates for multidimensional chaoses generated by symmetric random variables with logarithmically concave tails
JO - Banach Center Publications
PY - 2006
VL - 72
IS - 1
SP - 161
EP - 176
AB - Two kinds of estimates are presented for tails and moments of random multidimensional chaoses $S = ∑ a_{i₁,..., i_{d}} X_{i₁}^{(1)} ⋯ X_{i_{d}}^{(d)}$ generated by symmetric random variables $X_{i₁}^{(1)},...,X_{i_{d}}^{(d)}$ with logarithmically concave tails. The estimates of the first kind are generalizations of bounds obtained by Arcones and Giné for Gaussian chaoses. They are exact up to constants depending only on the order d. Unfortunately, suprema of empirical processes are involved. The second kind estimates are based on comparison between moments of S and moments of some related Rademacher chaoses. The estimates for pth moment are exact up to a factor $(max(1,ln p))^{d²}$.
LA - eng
KW - random chaos; moments
UR - http://eudml.org/doc/282330
ER -