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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.

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
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