On Feller processes with sample paths in Besov spaces

Abstract.

Under mild regularity assumptions on its domain the infinitesimal generator of a Feller process is known to be a pseudo-differential operator. We give a simple condition on the symbol of the generator in order to characterize the smoothness of the sample paths of real-valued Feller processes in terms of Besov spaces $B^s_{pq}({\Bbb R})$. Our result extends previous papers on the paths of Gaussian, symmetric $\alpha$-stable [6], [20], and Lévy processes [11].