Brownian motion, reflection groups and Tanaka formula

Nizar Demni; Dominique Lépingle

doi:10.4171/RSMUP/127-3

Brownian motion, reflection groups and Tanaka formula

Nizar Demni, Dominique Lépingle

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 of the distances from the initial process to the facets.

Original language	English (US)
Pages (from-to)	41-55
Number of pages	15
Journal	Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Volume	127
DOIs	https://doi.org/10.4171/RSMUP/127-3
State	Published - 2012

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics
Geometry and Topology

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AB - 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 of the distances from the initial process to the facets.

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ER -

Brownian motion, reflection groups and Tanaka formula

Abstract

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