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Applications de la théorie spectral des cordes vibrantes aux fonctionnelles additives principales d’un brownien réfléchi. (Applications of the spectral theory of vibrating strings to principal additive functionals of a reflected Brownian motion). (French) Zbl 0694.60070
The author characterizes the Fourier transforms and calculates Lévy measures of the processes with homogeneous independent increments defined by the principal additive functionals of a reflected Brownian motion taken at the inverse of its local time. For this the problem is nontrivially reduced to the case of increasing additive functionals and Krein’s spectral theory of vibrating strings is used.
Reviewer: R.Mikulevičius

MSC:
60J55 Local time and additive functionals
60E07 Infinitely divisible distributions; stable distributions
34B05 Linear boundary value problems for ordinary differential equations
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