Hitting times of hyperbolic Bessel processes

Abstract

We investigate the first hitting time to a point of a hyperbolic Bessel process which is the generalization of the radial part of Brownian motion on a hyperbolic space. We give the Laplace transform of the hitting time and the probability that the hyperbolic Bessel process reaches a given point in some time. Moreover, the limiting behavior of the expectation of the hitting time is computed. These results are improvements of some preceding results.