Berry–Esseen bound for the Brownian motions on hyperbolic spaces
Volume 277 / 2024
Studia Mathematica 277 (2024), 213-241
MSC: Primary 60F05; Secondary 58J65
DOI: 10.4064/sm230909-2-8
Published online: 26 September 2024
Abstract
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.
