Hitting half-spaces or spheres by the Ornstein-Uhlenbeck type diffusions
Probability
2011-11-04 v2
Abstract
The purpose of the paper is to provide a general method for computing hitting distributions of some regular subsets D for Ornstein-Uhlenbeck type operators of the form 1/2\Delta + F\cdot\nabla, 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 the paper is based on stochastic calculus and on skew product representation of multidimensional Brownian motion and yields more complete results as those based on Feynmann-Kac technique.
Cite
@article{arxiv.1109.0182,
title = {Hitting half-spaces or spheres by the Ornstein-Uhlenbeck type diffusions},
author = {Tomasz Byczkowski and Jakub Chorowski and Piotr Graczyk and Jacek Malecki},
journal= {arXiv preprint arXiv:1109.0182},
year = {2011}
}
Comments
22 pages