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Function Spaces as Path Spaces of Feller Processes

✍ Scribed by René L. Schilling

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
335 KB
Volume
217
Category
Article
ISSN
0025-584X

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✦ Synopsis

Let {Xt} t≥0 be a Feller process with infinitesimal generator (A, D(A)). If the test functions are contained in D(A), -A|C ∞ c (IR n ) is a pseudo -differential operator p(x, D) with symbol p(x, ξ). We investigate local and global regularity properties of the sample paths t → Xt in terms of (weighted) Besov B s pq (IR, ρ) and Triebel -Lizorkin F s pq (IR, ρ) spaces. The parameters for these spaces are determined by certain indices that describe the asymptotic behaviour of the symbol p(x, ξ). Our results improve previous papers on Lévy [5, 9] and Feller processes [22]. D(A) := {u ∈ C ∞ (IR n ) : the above limit exists strongly in C ∞ (IR n )} .

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