We give some limit theorems for the occupation times of 1-dimensional Brownian motion in some anisotropic Besov space. Our results generalize those obtained by Csaki et [] in continuous functions space.
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...
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