Function spaces as path spaces of Feller processes
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Submission date: 04. Dec. 1997
published in: Mathematische Nachrichten, 217 (2000), p. 147-174
MSC-Numbers: 60G17, 46E35, 60J75, 60J30
Keywords and phrases: feller process, besov space, triebel-lizorkin space, pseudo-differential operator, path properties
Let be a Feller process taking values in and with infinitesimal generator (A,D(A)). If the test functions are contained in D(A), is a pseudo-differential operator p(x,D) with symbol . We investigate local and global regularity properties of the sample paths in terms of (weighted) Besov and Triebel-Lizorkin spaces. The parameters for these spaces are determined by certain indices that describe the asymptotic behaviour of the symbol . Our results improve previous papers of Ciesielski et al. (Studia Math. 107, pp. 171-204), Roynette (Stochastics and Stochastics Reports 43, pp. 221-260), and Herren (Potential Analysis 7, pp. 689-704) on Lévy processes and Schilling (Math. Ann., to appear) on general Feller processes.