Excursions browniennes et carrés de processus de Bessel (Brownian excursions and squares of Bessel processes). (French) Zbl 0589.60070

Le Gall, Jean-François; Yor, Marc

C. R. Acad. Sci., Paris, Sér. I 303, 73-76 (1986).

Summary: We consider the sum of a reflected Brownian motion and a multiple of its local time at 0. The family of the local times associated with this process is distributed as the square of a d-dimensional Bessel process, where d depends on the above multiplicative constant. The two-parameter family of these local times is closely linked with the asymptotics of the windings of a three-dimensional Brownian motion.

MSC:

60J65	Brownian motion
60J55	Local time and additive functionals
60J60	Diffusion processes

Keywords:

reflected Brownian motion; local time; Bessel process; windings