Rendiconti del Seminario Matematico della Università di Padova

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

Published online: 2012-12-17

Brownian Motion, Reflection Groups and Tanaka Formula

Nizar Demni[1] and Dominique Lépingle[2]

(1) Université de Rennes I, France
(2) Université d'Orléans, 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