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Revista Matemática Iberoamericana

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

Published online: 2007-04-30

Poisson kernels of half–spaces in real hyperbolic spaces

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

(1) Wrocław University of Technology, Wroclaw, Poland
(2) Université d'Angers, Angers, France
(3) Université Blaise Pascal, Aubière, 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 Tomasz, Graczyk Piotr, Stós Andrzej: Poisson kernels of half–spaces in real hyperbolic spaces. Rev. Mat. Iberoam. 23 (2007), 85-126. doi: 10.4171/RMI/487