Two-sided moment estimates for a class of nonnegative chaoses

Abstract

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: $\lv X_i \rv_{2p} \leq A \lv X_i \rv_p$ for any $i$ and $p\ge 1$. 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.

References in corpus (2)

• A note on suprema of canonical processes based on random variables with regular moments
• Moment estimates for chaoses generated by symmetric random variables with logarithmically convex tails

Cited by in corpus (1)

• Concentration inequalities for polynomials in $\alpha$-sub-exponential random variables