Moments of Gaussian chaoses in Banach spaces

Abstract

We derive moment and tail estimates for Gaussian chaoses of arbitrary order with values in Banach spaces. We formulate a conjecture regarding two-sided estimates and show that it holds in a certain class of Banach spaces including L_q spaces. As a corollary we obtain two-sided bounds for moments of chaoses with values in L_q spaces based on exponential random variables.

References in corpus (2)

• The Johnson-Lindenstrauss lemma is optimal for linear dimensionality reduction
• Hanson-Wright inequality in Banach spaces