Théorèmes limites pour certaines fonctionnelles associées aux processus stables sur l'espace de Hölder.
In this paper we study the Hölder regularity property of the local time of a symmetric stable process of index 1 < α ≤ 2 and of its fractional derivative as a doubly indexed process with respect to the space and the time variables. As an application we establish some limit theorems for occupation times of one-dimensional symmetric stable processes in the space of Hölder continuous functions. Our results generalize those obtained by Fitzsimmons and Getoor for stable processes in the space...