Sharp inequalities involving multiplicative chaos sums

2022/12/11 by G. A. Karagulyan, Karagulyan, Grigori A.
Mathematics · #42A55 #42C05 #42C10 #60G42 #60G48 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2212.05431

openalex publication_date 2022/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeKar4, 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.

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