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April, 2007 Poisson kernels of half-spaces in real hyperbolic spaces
Tomasz Byczkowski, Piotr Graczyk, Andrzej Stós
Rev. Mat. Iberoamericana 23(1): 85-126 (April, 2007).


We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space $\mathbb{H}^n$. This enables us to find asymptotic properties of the kernel. We also show convergence to the Poisson kernel of the whole space $\mathbb{H}^n$. For $n=3$, $4$ or $6$ we compute explicit formulas for the Poisson kernel itself.


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Tomasz Byczkowski. Piotr Graczyk. Andrzej Stós. "Poisson kernels of half-spaces in real hyperbolic spaces." Rev. Mat. Iberoamericana 23 (1) 85 - 126, April, 2007.


Published: April, 2007
First available in Project Euclid: 1 June 2007

zbMATH: 1161.60024
MathSciNet: MR2351127

Primary: 60J45
Secondary: 58J65

Keywords: Brownian motion , hyperbolic spaces , Poisson kernel

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 1 • April, 2007
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