Open Collections

Two-sided moment estimates for random chaoses.

Banff International Research Station for Mathematical Innovation and Discovery

Let $X_1,\ldots,X_n$ be random variables such that there exists a constant $C>1$ satisfying $\|X_i\|_{2p} \leq C \|X_i\|_p$ for every $p \geq 1$. We define random chaos $S=\sum a_{i_1,...,i_d} X_{i_1}\cdots X_{i_d}$. We will show two-sided deterministic bounds on $||S||_p$, with constant depending only on $C$ and $d$ in two cases: 1) $X_1,\ldots,X_n$ are nonnegative and $a_{i_1,...,i_d}\geq 0$. 2) $X_1,\ldots ,X_n$ are symmetric, $d=2$.

Mathematics; Probability theory and stochastic processes; Statistics; Probability / statistical mechanics

video/mp4

Author affiliation: University of Warsaw

2017-11-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63734

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/