The main objective of the work is to provide sharp two-sided estimates of the λ-Green function, λ ≥ 0, of the hyperbolic Brownian motion of a half-space. We rely on the recent results obtained by K. Bogus and J. Małecki (2015), regarding precise estimates of the Bessel heat kernel for half-lines. We also substantially use the results of H. Matsumoto and M. Yor (2005) on distributions of exponential functionals of Brownian motion.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-3-1,
author = {Kamil Bogus and Tomasz Byczkowski and Jacek Ma\l ecki},
title = {Sharp estimates of the Green function of hyperbolic Brownian motion},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {197-221},
zbl = {1335.60149},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-3-1}
}
Kamil Bogus; Tomasz Byczkowski; Jacek Małecki. Sharp estimates of the Green function of hyperbolic Brownian motion. Studia Mathematica, Tome 231 (2015) pp. 197-221. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-3-1/