Harmonic measures of the half-plane and balls for the hyperbolic Brownian motion and Ornstein-Uhlenbeck diffusions

Abstract : The purpose of the paper is to provide integral representations of the Poisson kernel for a half-space and balls for hyperbolic Brownian motion and for the classical Ornstein-Uhlenbeck process. The method of proof is based on Girsanov's theorem and yields more complete results as those based on Feynmann-Kac technique.