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

• Autorzy: Tomasz Byczkowski , Jakub Chorowski , Piotr Graczyk , Jacek Małecki
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60G15: Gaussian processes
• 60J45: Probabilistic potential theory
• 60G40: Stopping times; optimal stopping problems; gambling theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 129
• Numer: 2
• Strony: 145-171

Daty

wydano

2012

Twórcy

autor

Tomasz Byczkowski

• Institute of Mathematics and Computer Sciences, Wrocław University of Technology, 50-370 Wrocław, Poland

autor

Jakub Chorowski

• Institute of Mathematics and Computer Sciences, Wrocław University of Technology, 50-370 Wrocław, Poland

autor

Piotr Graczyk

• Département de Mathématiques, Université d'Angers, 49045 Angers Cedex 01, France

autor

Jacek Małecki

• Institute of Mathematics and Computer Sciences, Wrocław University of Technology, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/cm129-2-1