Estimates of moments and tails of Gaussian chaoses

Rafał Latała

doi:10.1214/009117906000000421

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Home > Journals > Ann. Probab. > Volume 34 > Issue 6 > Article

November 2006 Estimates of moments and tails of Gaussian chaoses

Rafał Latała

Ann. Probab. 34(6): 2315-2331 (November 2006). DOI: 10.1214/009117906000000421

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Abstract

We derive two-sided estimates on moments and tails of Gaussian chaoses, that is, random variables of the form ∑a_{i₁,…,i_d}g_i₁⋯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. "Estimates of moments and tails of Gaussian chaoses." Ann. Probab. 34 (6) 2315 - 2331, November 2006. https://doi.org/10.1214/009117906000000421