Potential theory of hyperbolic Brownian motion in tube domains

Grzegorz Serafin. "Potential theory of hyperbolic Brownian motion in tube domains." Colloquium Mathematicae 135.1 (2014): 27-52. <http://eudml.org/doc/284374>.

@article{GrzegorzSerafin2014,
abstract = {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 $ℝ^\{n-1\}$. We show how to obtain formulas for these functions using analogous objects for the standard Brownian motion in $ℝ^\{2n\}$. We give formulas and uniform estimates for the set $D_a = \{x ∈ ℍⁿ:x₁ ∈ (0,a)\}$. The constants in the estimates depend only on the dimension of the space.},
author = {Grzegorz Serafin},
journal = {Colloquium Mathematicae},
keywords = {hyperbolic space; hyperbolic Brownian motion; tube domains; strip; Poisson kernel; Green function; uniform estimates},
language = {eng},
number = {1},
pages = {27-52},
title = {Potential theory of hyperbolic Brownian motion in tube domains},
url = {http://eudml.org/doc/284374},
volume = {135},
year = {2014},
}

TY - JOUR
AU - Grzegorz Serafin
TI - Potential theory of hyperbolic Brownian motion in tube domains
JO - Colloquium Mathematicae
PY - 2014
VL - 135
IS - 1
SP - 27
EP - 52
AB - 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 $ℝ^{n-1}$. We show how to obtain formulas for these functions using analogous objects for the standard Brownian motion in $ℝ^{2n}$. We give formulas and uniform estimates for the set $D_a = {x ∈ ℍⁿ:x₁ ∈ (0,a)}$. The constants in the estimates depend only on the dimension of the space.
LA - eng
KW - hyperbolic space; hyperbolic Brownian motion; tube domains; strip; Poisson kernel; Green function; uniform estimates
UR - http://eudml.org/doc/284374
ER -