Strong approximation of some additive functionals of symmetric stable process

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.