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Estimates of moments and tails of Gaussian chaoses

Rafał Latała
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Abstract

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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Rafał Latała. 2007-02-28. Estimates of moments and tails of Gaussian chaoses. https://doi.org/10.1214/009117906000000421

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