Tail and moment estimates for a class of random chaoses of order two
Volume 249 / 2019
Studia Mathematica 249 (2019), 1-32
MSC: Primary 60E15.
DOI: 10.4064/sm170819-2-5
Published online: 6 March 2019
Abstract
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 $\lVert X \rVert_{2p} \leq \alpha \lVert X \rVert_p$ for any $p\geq 1$ and some $\alpha\geq 1$. Estimates are deterministic and exact up to some multiplicative constants which depend only on $\alpha$.
