Limit Theorems for a Class of Additive Functionals of Symmetric Stable Process and Fractional Brownian Motion in Besov-Orlicz Spaces

Abstract

We use the Potter's Theorem and the tightness criterion in Besov-Orlicz spaces, recently proved, to generalize some limit theorem for occupation times problem of certain self-similar process, namely symmetric stable process of index 1<α≤ and fractional Brownian motion of Hurst parameter 0<H<1. We give also strong approximation version of our limit theorem, more precisely, we show L^p-estimate version.