Estimates of moments and tails of Gaussian chaoses

Details Estimates of moments and tails of Gaussian chaoses Estimates of moments and tails of Gaussian chaoses

2005-05-15

arxiv.org/abs/math/0505313v2

Annals of Probability 2006, Vol. 34, No. 6, 2315-2331

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000421 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000421

We derive two-sided estimates on moments and tails of Gaussian chaoses, that
is, random variables of the form $\sum a_{i_1,...,i_d}g_{i_1}... g_{i_d}$,
where $g_i$ are i.i.d. ${\mathcal{N}}(0,1)$ r.v.'s. Estimates are exact up to
constants depending on $d$ only.

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