Un critère de tension dans les espaces de Besov-Orlicz et applications au problème du temps d'occupation Volume 18, n o 2 (2011), p. 301-321. © Annales mathématiques Blaise Pascal, 2011, tous droits réservés. L'accès aux articles de la revue « Annales mathématiques Blaise Pascal » (http://ambp.cedram.org/), implique l'accord avec les conditions générales d'utilisation (http://ambp.cedram.org/legal/). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

In this paper we prove two main results. The rst one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index 1 < ≤ 2. Our result is similar to that of Marcus and Rosen in 1992 for local time. The second result is to give a ( , )-variation of fractional derivatives of local time of symmetric stable process with index 1 < ≤ 2. Our approach is similar to that of Eisenbaum in 2000 for local time.

In this paper, we prove two main results. The first one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index 1 <ˇÄ 2; our result is similar to that of Marcus and Rosen (1992) for local time. The second result is to give a p; q-variation of fractional derivatives of local time of symmetric stable process with index 1 <ˇÄ 2. Our approach is similar to that of Eisenbaum (2000) for local time.

No abstract

Abstract. This paper deals with some additive functionals based on the local time of symmetric stable process. In concrete, we obtain some L p -inequalities of the local time and the fractional derivative of the local time of symmetric stable process of index 1 < α 2 . As an application, we generalize the well known Barlow-Yor [4] inequality, which we use to give a strong approximation version, (almost surely estimate), of occupation times problem of this process. Our results generalize those obtained by Csaki et al. [7] for Brownian motion, and Ait Ouahra and Ouali [2] for symmetric stable process of index 1 < α 2 in L p -norm.Mathematics subject classification (2010): 60J55.