Estimates of moments and tails of Gaussian chaoses. (English) Zbl 1119.60015

The author derives precise bounds on the moments and tails of Gaussian chaoses of order \(d\), that is, random variables of the form \(\sum_{i_1 < \dots <i_d}a_{i_1,\dots,i_d}g_{i_1}\dots g_{i_d},\) where \(g_i\) are independent standard normal random variables. The bounds are exact up to constants depending on \(d\) only.


60E15 Inequalities; stochastic orderings
60G15 Gaussian processes
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