Let X = X(t); t ≥ 0 be the hyperbolic Brownian motion on the real hyperbolic space ℍⁿ = x ∈ ℝⁿ:xₙ > 0. We study the Green function and the Poisson kernel of tube domains of the form D × (0,∞)⊂ ℍⁿ, where D is any Lipschitz domain in . We show how to obtain formulas for these functions using analogous objects for the standard Brownian motion in . We give formulas and uniform estimates for the set . The constants in the estimates depend only on the dimension of the space.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm135-1-3,
author = {Grzegorz Serafin},
title = {Potential theory of hyperbolic Brownian motion in tube domains},
journal = {Colloquium Mathematicae},
volume = {135},
year = {2014},
pages = {27-52},
zbl = {1302.60114},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm135-1-3}
}
Grzegorz Serafin. Potential theory of hyperbolic Brownian motion in tube domains. Colloquium Mathematicae, Tome 135 (2014) pp. 27-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm135-1-3/