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Fractional derivatives of local times of stable Lévy processes as the limits of the occupation time problem in Besov space

Ouhara M. A., Eddahbi M., Ouali M.

Probability and Mathematical Statistics

2004

Vol. 24, Fasc. 2

263--279

In this paper, we firstly study the Besov regularity of the local time of symmetric stable processes and of its fractional derivative. Secondly, we establish limit theorems for occupation times of α-symmetric stable processes with 1 < α ≤ 2 in some Besov spaces. Finally, we give the strong approximation version of our limit theorems.