Tail and moment estimates for some types of chaos
Volume 135 / 1999
Studia Mathematica 135 (1999), 39-53
DOI: 10.4064/sm-135-1-39-53
Abstract
Let $X_i$ be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable $X= ∑_{i ≠ j}a_{i,j}X_iX_j$, where $a_{i,j}$ are real numbers. We derive approximate formulas for the tails and moments of X and of its decoupled version, which are exact up to some universal constants.
