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On Potential Theory of Hyperbolic Brownian Motion with Drift

Serafin Grzegorz

Probability and Mathematical Statistics

2020

Vol. 40, Fasc. 1

1--22

Consider the λ-Green function and the λ-Poisson kernel of a Lipschitz domain U ⊂ Hn = {x ∈ Rn: xn > 0} for hyperbolic Brownian motion with drift. We provide several relationships that facilitate studying those objects and explain somewhat their nature. As an application, we yield uniform estimates for sets of the form Sa,b = {x ∈ Hn : xn > a, x1 ∈ (0, b)}, a, b > 0, which covers and extends existing results of that kind.