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Function Spaces as Path Spaces of Feller Processes
Author(s) -
Schilling René L.
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200009)217:1<147::aid-mana147>3.0.co;2-r
Subject(s) - mathematics , generator (circuit theory) , path (computing) , pure mathematics , hardy space , operator (biology) , infinitesimal , function (biology) , differential operator , mathematical analysis , power (physics) , biochemistry , physics , chemistry , repressor , quantum mechanics , evolutionary biology , biology , computer science , transcription factor , gene , programming language
Let { X t } t ≥ 0 be a Feller process with infinitesimal generator ( A , D ( A )). If the test functions are contained in D ( A ), — A | C ∞ c (ℝ n ) is a pseudo–differential operator p ( x , D ) withsymbol p ( x , ξ ). We investigate local and global regularity properties of the sample paths t ↦ X t in terms of (weighted) Besov B s pq (ℝ, ρ ) and Triebel–Lizorkin F s pq (ℝ, 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].