Using explicit representations of the Brownian motions on hyperbolic spaces, we show that their almost sure convergence and the central limit theorems for the radial components as time tends to infinity can be easily obtained. We also give a straightforward strategy to obtain explicit expressions for the limit distributions or Poisson kernels.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-3,
author = {H. Matsumoto},
title = {Limiting behaviors of the Brownian motions on hyperbolic spaces},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {193-215},
zbl = {1193.58021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-3}
}
H. Matsumoto. Limiting behaviors of the Brownian motions on hyperbolic spaces. Colloquium Mathematicae, Tome 120 (2010) pp. 193-215. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-3/