On Feller processes with sample paths in Besov spaces (Q1380091)

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 \(B^s_{pq}(\mathbb{R})\). Our result extends previous papers on the paths of Gaussian, symmetric \(\alpha\)-stable processes [see \textit{Z. Ciesielski}, \textit{G. Kerkyacharian} and \textit{B. Roynette}, Stud. Math. 107, No. 2, 171-204 (1993; Zbl 0809.60004) and \textit{B. Roynette}, Stochastics Stochastics Rep. 43, No. 3/4, 221-260 (1993; Zbl 0808.60071)], and Lévy processes [see \textit{V. Herren}, Potential Anal. 7, No. 3, 689-704 (1997)].