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Brownian motion, reflection groups and Tanaka formula. (English) Zbl 1263.60074
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.
60J65 Brownian motion
60G44 Martingales with continuous parameter
60J55 Local time and additive functionals
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