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Zbl 1060.60082
Carmona, Philippe; Petit, Frédérique; Yor, Marc
A trivariate law for certain processes related to perturbed Brownian motions. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 40, No. 6, 737-758 (2004). ISSN 0246-0203

Williams' path decomposition and Pitman's representation theorem for BES(3) are expressions of some deep relations between reflecting Brownian motion and the three-dimensional Bessel processes. The authors [Stochastic Processes Appl. 79, 323--333 (1999; Zbl 0965.60074)] presented an attempt to relate better reflecting Brownian motion and the two-dimensional Bessel process, using space and time changes related to Ray-Knight theorems on local times, in the manner of {\it T. Jeulin} [in: Grossissements de filtrations: exemples et applications. Lect. Notes Math. 1118, 197--304 (1985; Zbl 0562.60080)] and {\it Ph. Biane} and {\it M. Yor} [Bull. Sci. Math., II. Sér. 111, 23--101 (1987; Zbl 0619.60072)]. In this paper the law of a triplet linked to the perturbed Brownian motion which naturally arises in [the authors, loc. cit.] is characterized, and its relations with Bessel processes of several dimensions are pointed out. The results provide some new understanding of the generalizations of P. Lévy's arcsine law for perturbed Brownian motions previously obtained by the second author.
[Pavel Gapeev (Moskva)]

MSC 2000:: *60J65 Brownian motion
60J60 Diffusion processes
60J55 Additive functionals
60J25 Markov processes with continuous parameter

Keywords: reflecting Brownian motion; Bessel processes; Ray-Knight theorems; generalized arcsine laws

Citations: Zbl 0965.60074; Zbl 0562.60080; Zbl 0619.60072

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