Brownian motion, reflection groups and Tanaka formula

Nizar Demni; Dominique Lépingle

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arXiv · 1101.0522

Brownian motion, reflection groups and Tanaka formula

Nizar Demni·Dominique Lépingle

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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 at zero of the distances from the initial process to the facets.

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Nizar Demni, Dominique Lépingle. 2011-01-03. Brownian motion, reflection groups and Tanaka formula. https://arxiv.org/abs/1101.0522

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