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Tail and moment estimates for a class of random chaoses of order two

Volume 249 / 2019

Rafał Meller 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 $\alpha$.

Authors

  • Rafał MellerInstitute of Mathematics
    University of Warsaw
    02-097 Warszawa, Poland
    e-mail

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