Hitting half-spaces by Bessel-Brownian di usions

The purpose of the paper is to nd explicit formulas describing the joint distributions of the rst hitting time and place for half-spaces of codimension one for a di usion in R, composed of onedimensional Bessel process and independent n-dimensional Brownian motion. The most important argument is carried out for the two-dimensional situation. We show that this amounts to computation of distributions of various integral functionals with respect to a two-dimensional process with independent Bessel components. As a result, we provide a formula for the Poisson kernel of a half-space or of a strip for the operator (I −∆), 0 < α < 2. In the case of a half-space, this result was recently found, by di erent methods, in [6]. As an application of our method we also compute various formulas for rst hitting places for the isotropic stable Lévy process.