Boundedness of Gaussian random sums on rooted homogeneous trees

Yong Han^a, Yabqi Qiu^bc, Zipeng Wang<sup>d

a</sup> College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, Guangdong, China
^b Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China
^c School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
^d College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

Abstract: 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.

Key words and phrases: gaussian processes, boundedness and continuity, uniform convergence.

MSC: Primary 60G15; Secondary 06A06, 05C05

Language: English

DOI: 10.17323/1609-4514-2024-24-4-587-601