2011/01/03 by Nizar Demni, Demni, Nizar, Dominique Lépingle +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1101.0522
arxiv created 2011/01/03 · openalex publication_date 2011/01/03 · arxiv updated 2011/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka's formula for linear Brownian motion. The paper is closed with a description of the boundary process through the local times at zero of the distances from the initial process to the facets.