On Feller processes with sample paths in Besov spaces
type: Item
instance of: scholarly article
title: On Feller processes with sample paths in Besov spaces
zbMATH Open document ID: 0888.60036
published in: Mathematische Annalen
publication date: 1998-05-25T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 35S99
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 1121716
zbMATH Keywords: Feller process
zbMATH Keywords: pseudo-differential operator
zbMATH Keywords: smoothness of the sample paths
zbMATH Keywords: Besov spaces
zbMATH Keywords: Lévy processes
author: R. L. Schilling
MaRDI profile type: Publication
full work available at URL: s002080050132
OpenAlex ID: W2058417978
DOI: 10.1007/S002080050132
description: scientific article; zbMATH DE number 1121716