Moscow Mathematical Journal

Volume 24, Issue 4, October–December 2024 pp. 587–601.

Boundedness of Gaussian Random Sums on Rooted Homogeneous Trees

Authors: Yong Han (1), Yanqi Qiu (2), and Zipeng Wang (3)
Author institution:(1) College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, Guangdong, China
(2) School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China; Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China
(3) College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

Summary:

Let $q\geq 2$ be an integer and let $\mathcal{T}_q$ be a rooted $q$-homogeneous tree. Using Marcus–Pisier's approach to the uniform convergence of random Fourier series on compact Abelian groups, we obtain a necessary and sufficient condition for the almost sure boundedness of a class of $\mathcal{T}_q$-indexed Gaussian process.

2020 Math. Subj. Class. Primary: 60G15; Secondary: 06A06, 05C05.

Keywords: Gaussian processes, boundedness and continuity, uniform convergence.

Contents Full-Text PDF