Poisson kernels of half-spaces in real hyperbolic spaces

2005/03/17 by T. Byczkowski, Byczkowski, T., P. Graczyk +3
Mathematics · #58J65 #60J45 #60J65 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:58J65 #msc:60J45 #msc:60J65

paper · pdf · doi:10.48550/arxiv.math/0503372

arxiv created 2005/03/17 · arxiv updated 2009/12/01

Abstract

We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space \Hⁿ. This enables us to find asymptotic properties of the kernel. Our starting point is the formula for its Fourier transform. When n=3, 4 or 6 we give an explicit formula for the Poisson kernel itself. In the general case we give various asymptotics and show convergence to the Poisson kernel of \Hⁿ.

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