Limiting behaviors of the Brownian motions on hyperbolic spaces

Volume 119 / 2010

H. Matsumoto Colloquium Mathematicum 119 (2010), 193-215 MSC: 58J65, 60J60. DOI: 10.4064/cm119-2-3


Using explicit representations of the Brownian motions on hyperbolic spaces, we show that their almost sure convergence and the central limit theorems for the radial components as time tends to infinity can be easily obtained. We also give a straightforward strategy to obtain explicit expressions for the limit distributions or Poisson kernels.


  • H. MatsumotoGraduate School of Information Science
    Nagoya University
    Chikusa-ku, Nagoya 464-8601, Japan
    Department of Mathematical Sciences
    Faculty of Science
    Yamagata University
    1-4-12 Kojirakawa-machi
    Yamagata 990-8560, Japan

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