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Brownian motion, reflection groups and Tanaka formula

Authors
  • Demni, Nizar
  • Lépingle, Dominique
Publication Date
Jan 01, 2012
Source
HAL
Keywords
Language
English
License
Unknown
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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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