D\'evissage of a Poisson boundary under equivariance and regularity conditions
Probability
2013-11-19 v1 Dynamical Systems
Abstract
We present a method that allows, under suitable equivariance and regularity conditions, to determine the Poisson boundary of a diffusion starting from the Poisson boundary of a sub-diffusion of the original one. We then give two examples of application of this d\'evissage method. Namely, we first recover the classical result that the Poisson boundary of Brownian motion on a rotationally symmetric manifolds is generated by its escape angle, and we then give an "elementary" probabilistic proof of the delicate result of [Bai08], i.e. the determination of the Poisson boundary of the relativistic Brownian motion in Minkowski space-time.
Keywords
Cite
@article{arxiv.1311.4428,
title = {D\'evissage of a Poisson boundary under equivariance and regularity conditions},
author = {Jürgen Angst and Camille Tardif},
journal= {arXiv preprint arXiv:1311.4428},
year = {2013}
}
Comments
20 pages, 3 figures