Preprint 42/1997

Function spaces as path spaces of Feller processes

Rene Schilling

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Submission date: 04. Dec. 1997
Pages: 28
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 img1 be a Feller process taking values in img2 and with infinitesimal generator (A,D(A)). If the test functions are contained in D(A), img3 is a pseudo-differential operator p(x,D) with symbol img4. We investigate local and global regularity properties of the sample paths img5 in terms of (weighted) Besov img6 and Triebel-Lizorkin img7 spaces. The parameters for these spaces are determined by certain indices that describe the asymptotic behaviour of the symbol img8. 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.

24.11.2021, 02:10