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Fractional derivatives of local times of stable Lévy processes as the limits of the occupation time problem in Besov space. (English) Zbl 1080.60074
The authors consider a symmetric stable process $$X$$ of index $$\alpha\in(1,2]$$ and its local time. Firstly they study the Besov regularity of the local time and of its fractional derivative. Secondly they prove weak and strong limit theorems for occupation times of the process $$X$$ in some Besov spaces.

##### MSC:
 60J55 Local time and additive functionals 60F05 Central limit and other weak theorems 60G52 Stable stochastic processes 46E15 Banach spaces of continuous, differentiable or analytic functions
##### Keywords:
symmetric stable processes