Revista Matemática Iberoamericana


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Volume 23, Issue 1, 2007, pp. 85–126
DOI: 10.4171/RMI/487

Poisson kernels of half–spaces in real hyperbolic spaces

Tomasz Byczkowski[1], Piotr Graczyk[2] and Andrzej Stós[3]

(1) Institute of Mathematics, Wrocław University of Technology, Wyb. Wyspianskiego 27, 50-370, WROCLAW, POLAND
(2) Département de Mathématiques, Université d'Angers, 2, boulevard Lavoisier, 49045, ANGERS CEDEX, FRANCE
(3) Laboratoire de Mathématiques, UMR 6620, Université Blaise Pascal, Campus des Cézeaux, 24, avenue des Landais, 63177, AUBIÈRE CEDEX, FRANCE

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.

Keywords: Hyperbolic spaces, Brownian motion, Poisson kernel

Byczkowski T, Graczyk P, Stós A. Poisson kernels of half–spaces in real hyperbolic spaces. Rev. Mat. Iberoamericana 23 (2007), 85-126. doi: 10.4171/RMI/487