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Contents of PMS, Vol. 24, Fasc. 2,
pages 263 - 279
 

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 a -symmetric stable processes with 1 < a < 2 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.

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