Dévissage of a Poisson boundary under equivariance and regularity conditions

2013/11/18 by Jürgen Angst, Angst, Jürgen, Camille Tardif +1
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR) #Stochastic processes and financial applications #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.1311.4428

20 pages, 3 figures

arxiv created 2013/11/18 · openalex publication_date 2013/11/18 · arxiv updated 2013/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 dévissage 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.

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