- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:49
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2013)
127
2012
0
Brownian Motion, Reflection Groups and Tanaka Formula
Nizar
Demni
Université de Rennes I, RENNES CEDEX, FRANCE
Dominique
Lépingle
Université d'Orléans, 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.
General
41
55
10.4171/RSMUP/127-3
http://www.ems-ph.org/doi/10.4171/RSMUP/127-3