Hitting half-spaces or spheres by Ornstein–Uhlenbeck type diffusions
Colloquium Mathematicum, Tome 129 (2012) no. 2, pp. 145-171
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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\over 2}\varDelta + 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 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.
Keywords:
purpose paper provide general method computing hitting distributions regular subsets ornstein uhlenbeck type operators form vardelta cdot nabla bounded orthogonal boundary important application obtain integral representations poisson kernel half space balls hyperbolic brownian motion classical ornstein uhlenbeck process method developed paper based stochastic calculus skew product representation multidimensional brownian motion yields complete results those based feynman kac technique
Affiliations des auteurs :
Tomasz Byczkowski 1 ; Jakub Chorowski 1 ; Piotr Graczyk 2 ; Jacek Małecki 1
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author = {Tomasz Byczkowski and Jakub Chorowski and Piotr Graczyk and Jacek Ma{\l}ecki},
title = {Hitting half-spaces or spheres by {Ornstein{\textendash}Uhlenbeck} type diffusions},
journal = {Colloquium Mathematicum},
pages = {145--171},
year = {2012},
volume = {129},
number = {2},
doi = {10.4064/cm129-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm129-2-1/}
}
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Tomasz Byczkowski; Jakub Chorowski; Piotr Graczyk; Jacek Małecki. Hitting half-spaces or spheres by Ornstein–Uhlenbeck type diffusions. Colloquium Mathematicum, Tome 129 (2012) no. 2, pp. 145-171. doi: 10.4064/cm129-2-1
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