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

Tomasz Byczkowski (1) , Jakub Chorowski (1) , Piotr Graczyk (2) , Jacek Malecki (1, 2)

1 IMCS - Institute of Mathematics and Computer Science [Wroclaw]
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Domaines: Probabilités [math.PR]

Tomasz Byczkowski, Jakub Chorowski, Piotr Graczyk, Jacek Malecki. Harmonic measures of the half-plane and balls for the hyperbolic Brownian motion and Ornstein-Uhlenbeck diffusions. 2011. ⟨hal-00618026⟩