Rendiconti del Seminario Matematico della Università di Padova


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Volume 127, 2012, pp. 41–55
DOI: 10.4171/RSMUP/127-3

Brownian Motion, Reflection Groups and Tanaka Formula

Nizar Demni[1] and Dominique Lépingle[2]

(1) IRMAR, Université de Rennes I, Campus de Beaulieu, 35042, Rennes CEDEX, France
(2) MAPMO, UMR 6628, Université d'Orléans, B.P. 6759, 45067, Orléans CEDEX 2, France

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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Demni Nizar, Lépingle Dominique: Brownian Motion, Reflection Groups and Tanaka Formula. Rend. Sem. Mat. Univ. Padova 127 (2012), 41-55. doi: 10.4171/RSMUP/127-3