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

Bertoin, Jean

Ann. Inst. Henri Poincaré, Probab. Stat. 25, No. 3, 307-323 (1989).

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

Keywords:

additive functionals; reflected Brownian motion; local time; vibrating strings