Sharp estimates of the Green function of hyperbolic Brownian motion
Volume 228 / 2015
Studia Mathematica 228 (2015), 197-221 MSC: Primary 60J65; Secondary 58J65. DOI: 10.4064/sm228-3-1
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.