Estimates of moments and tails of Gaussian chaoses

摘要

We derive two-sided estimates on moments and tails of Gaussian chaoses, that is, random variables of the form Sigma a(i1),...,i(d)g(i1) center dot center dot center dot g(id), where g(i) are i.i.d. N(0, 1) r.v.s. Estimates are exact up to constants depending on d only.