Berry-Esseen bound for the Brownian motions on hyperbolic spaces

被引：0

作者：

Shiozawa, Yuichi ^{[1
]}

机构：

[1] Doshisha Univ, Fac Sci & Engn, Dept Math Sci, Kyoto 6100394, Japan

来源：

STUDIA MATHEMATICA | 2024年 / 277卷 / 03期

关键词：

Berry-Esseen bound; Brownian motion; hyperbolic space; Millson formula; ASYMPTOTIC-BEHAVIOR; HEAT KERNEL;

D O I：

10.4064/sm230909-2-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain the uniform convergence rate for the Gaussian fluctuation of the radial part of the Brownian motion on a hyperbolic space. We also show that this result is sharp if the dimension of the hyperbolic space is 2 or general odd. Our approach is based on the repetitive use of the Millson formula and the integration by parts formula.

引用

页码：213 / 241

页数：30

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