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Brownian motion, reflection groups and Tanaka formula

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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https://hal.archives-ouvertes.fr/hal-00551333
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Submitted on : Monday, January 3, 2011 - 2:35:58 PM
Last modification on : Thursday, March 26, 2020 - 5:50:19 PM
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Nizar Demni, Dominique Lépingle. Brownian motion, reflection groups and Tanaka formula. Rendiconti del Seminario Matematico della Università di Padova, University of Padua / European Mathematical Society, 2012, 127, pp.41-55. ⟨10.4171/RSMUP/127-3⟩. ⟨hal-00551333⟩

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