Revista Matemática Iberoamericana

Poisson kernels of half-spaces in real hyperbolic spaces

Tomasz Byczkowski, Piotr Graczyk, and Andrzej Stós

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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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 23, Number 1 (2007), 85-126.

Dates
First available in Project Euclid: 1 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1180728886

Mathematical Reviews number (MathSciNet)
MR2351127

Zentralblatt MATH identifier
1161.60024

Subjects
Primary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]
Secondary: 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]

Keywords
hyperbolic spaces Brownian motion Poisson kernel

Citation

Byczkowski, Tomasz; Graczyk, Piotr; Stós, Andrzej. Poisson kernels of half-spaces in real hyperbolic spaces. Rev. Mat. Iberoamericana 23 (2007), no. 1, 85--126. https://projecteuclid.org/euclid.rmi/1180728886


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