Poisson kernels of half–spaces in real hyperbolic spaces
Copyright policy )Poisson kernels of half–spaces in real hyperbolic spaces
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.
- French National Centre for Scientific Research France
- University of Clermont Auvergne France
- Clermont Université France
- University of Wrocław Poland
- University of Angers France
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Diffusion processes and stochastic analysis on manifolds, Probability (math.PR), Poisson kernel, 58J65, Probabilistic potential theory, hyperbolic spaces, 60J45, FOS: Mathematics, 60J65, Brownian motion, 60J45; 60J65; 58J65, Mathematics - Probability
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Diffusion processes and stochastic analysis on manifolds, Probability (math.PR), Poisson kernel, 58J65, Probabilistic potential theory, hyperbolic spaces, 60J45, FOS: Mathematics, 60J65, Brownian motion, 60J45; 60J65; 58J65, Mathematics - Probability
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