FRACTIONAL DERIVATIVES OF LOCAL TIMES OF STABLE LÉVY
PROCESSES AS THE LIMITS OF THE OCCUPATION TIME PROBLEM IN
BESOV SPACE
M. Ait Ouahra
M. Eddahbi
M. Ouali
Abstract: 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 -symmetric stable processes with in some Besov
spaces. Finally, we give the strong approximation version of our limit theorems.
2000 AMS Mathematics Subject Classification: Primary 60J55, 60F05; Secondary
60G52, 46E15.
Key words and phrases: Stable processes, local time, fractional derivative, occupation
time problem, Besov space.