Hitting half-spaces or spheres by Ornstein-Uhlenbeck type diffusions

Tomasz Byczkowski, et al. "Hitting half-spaces or spheres by Ornstein-Uhlenbeck type diffusions." Colloquium Mathematicae 129.2 (2012): 145-171. <http://eudml.org/doc/284283>.

@article{TomaszByczkowski2012,
abstract = {The purpose of the paper is to provide a general method for computing the hitting distributions of some regular subsets D for Ornstein-Uhlenbeck type operators of the form 1/2Δ + F·∇, with F bounded and orthogonal to the boundary of D. As an important application we obtain 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 developed in this paper is based on stochastic calculus and on the skew product representation of multidimensional Brownian motion and yields more complete results than those based on the Feynman-Kac technique.},
author = {Tomasz Byczkowski, Jakub Chorowski, Piotr Graczyk, Jacek Małecki},
journal = {Colloquium Mathematicae},
keywords = {harmonic measure; Ornstein-Uhlenbeck diffusion; Girsanov theorem; hyperbolic spaces; Poisson kernel},
language = {eng},
number = {2},
pages = {145-171},
title = {Hitting half-spaces or spheres by Ornstein-Uhlenbeck type diffusions},
url = {http://eudml.org/doc/284283},
volume = {129},
year = {2012},
}

TY - JOUR
AU - Tomasz Byczkowski
AU - Jakub Chorowski
AU - Piotr Graczyk
AU - Jacek Małecki
TI - Hitting half-spaces or spheres by Ornstein-Uhlenbeck type diffusions
JO - Colloquium Mathematicae
PY - 2012
VL - 129
IS - 2
SP - 145
EP - 171
AB - The purpose of the paper is to provide a general method for computing the hitting distributions of some regular subsets D for Ornstein-Uhlenbeck type operators of the form 1/2Δ + F·∇, with F bounded and orthogonal to the boundary of D. As an important application we obtain 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 developed in this paper is based on stochastic calculus and on the skew product representation of multidimensional Brownian motion and yields more complete results than those based on the Feynman-Kac technique.
LA - eng
KW - harmonic measure; Ornstein-Uhlenbeck diffusion; Girsanov theorem; hyperbolic spaces; Poisson kernel
UR - http://eudml.org/doc/284283
ER -