Brownian motion, reflection groups and Tanaka formula (Q442626)

It is proved that a projection of a finite dimensional Wiener process (Brownian motion) on a closed Weyl chamber -- the term from finite reflection group theory -- is also a Wiener process reflected from the walls of the chamber. A decomposition of this reflected process is given, which may be regarded as a multidimensional extension of Tanaka's formula. The links to local times at the boundary are established. A brief introduction to finite reflection group theory is provided.