2015/02/02 by Serafin, Grzegorz
#60J65 60J60 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1502.00462
Consider the λ-Green function and the λ-Poisson kernel of a Lipschitz domain U⊂ \mathbb Hn=\x∈\mathbb Rn:xn>0\ for hyperbolic Brownian motion with drift. We provide several relationships that facilitate studying those objects and explain somehow theirs nature. As an application, we yield uniform estimates in case of sets of the form Sa,b=\x∈\mathbb Hn:xn>a, x1∈(0,b)\, a,b>0, a,b>0, which covers and extends existing results of that kind.