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Théorèmes limites pour certaines fonctionnelles associées aux processus stables sur l'espace de Hölder
Ouahra, M. Ait
Eddahbi, M.

Data: 2001
Resum: In this paper we study the Hölder regularity property of the local time of a symmetric stable process of index 1 < [alpha] [less than or equal] 2 and of its fractional derivative as a doubly indexed process with respect to the space and the time variables. As an application we establish some limit theorems for occupation times of one--dimensional symmetric stable processes in the space of Hölder continuous functions. Our results generalize those obtained by Fitzsimmons and Getoor for stable processes in the space on continuous functions. The limiting processes are fractional derivatives and Hilbert transforms of local times.
Drets: Tots els drets reservats.
Llengua: Francès
Document: article ; recerca ; Versió publicada
Publicat a: Publicacions matemàtiques, V. 45 N. 2 (2001) , p. 371-386, ISSN 2014-4350

Adreça original: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/38021
DOI: 10.5565/PUBLMAT_45201_04


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