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Sharp estimates of the Green function of hyperbolic Brownian motion

Volume 228 / 2015

Kamil Bogus, Tomasz Byczkowski, Jacek Małecki Studia Mathematica 228 (2015), 197-221 MSC: Primary 60J65; Secondary 58J65. DOI: 10.4064/sm228-3-1

Abstract

The main objective of the work is to provide sharp two-sided estimates of the $\lambda $-Green function, $\lambda \geq 0$, of the hyperbolic Brownian motion of a half-space. We rely on the recent results obtained by K. Bogus and J. Małecki (2015), regarding precise estimates of the Bessel heat kernel for half-lines. We also substantially use the results of H. Matsumoto and M. Yor (2005) on distributions of exponential functionals of Brownian motion.

Authors

  • Kamil BogusFaculty of Pure and Applied Mathematics
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Tomasz ByczkowskiInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    and
    Faculty of Pure and Applied Mathematics
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Jacek MałeckiFaculty of Pure and Applied Mathematics
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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