Sharp inequalities involving multiplicative chaos sums
Probability
2025-12-09 v1 Classical Analysis and ODEs
Abstract
The present note is an essential addition to the author's arxiv paper arXiv:2001.01070, concerning general multiplicative systems of random variables. Using some lemmas and the methodology of \cite{Kar4}, we obtain a general extreme inequality, with corollaries involving Rademacher chaos sums and those analogues for multiplicative systems. In particular we prove that a system of functions generated by bounded products of a multiplicative system is a convergence system.
Keywords
Cite
@article{arxiv.2212.05431,
title = {Sharp inequalities involving multiplicative chaos sums},
author = {Grigori A. Karagulyan},
journal= {arXiv preprint arXiv:2212.05431},
year = {2025}
}
Comments
The present note is an essential addition to the author's arxiv paper arXiv:2001.01070