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Limit theorems for some functionals associated with stable processes in a class of Besov spaces. (Théorèmes limites pour certaines fonctionnelles associées aux processus stables dans une classe d’espaces de Besov.) (French) Zbl 1015.60068
Summary: This paper studies limit theorems for the occupation times of one-dimensional symmetric stable processes. Our goal is to extend P. J. Fitzsimmons and R. K. Getoor’s results [Ann. Inst. Henri Poincaré, Probab. Stat. 28, No. 2, 311-333 (1992; Zbl 0749.60072)] and those of J. Rosen [in: Séminaire de probabilités XXV, Lect. Notes Math. 1485, 407-424 (1991; Zbl 0758.60078)], established in the uniform norm, to the Besov norm. The limit processes are fractional derivatives and Hilbert transforms of the stable local time.

MSC:
60J55 Local time and additive functionals
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