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