We derive two-sided bounds for moments of random multilinear forms (random chaoses) with nonnegative coeficients generated by independent nonnegative random variables X i which satisfy the following condition on the growth of moments: X i 2p ≤ A X i p for any i and p ≥ 1. Estimates are deterministic and exact up to multiplicative constants which depend only on the order of chaos and the constant A in the moment assumption.
We derive two-sided bounds for moments and tails of random quadratic forms (random chaoses of order 2), generated by independent symmetric random variables such that X 2p ≤ α X p for any p ≥ 1 and some α ≥ 1. Estimates are deterministic and exact up to some multiplicative constants which depend only on α.
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 Lq spaces. As a corollary we obtain two-sided bounds for moments of chaoses with values in Lq spaces based on exponential random variables.
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