Path regularity for Feller semigroups via Gaussian kernel estimates and generalizations to arbitrary semigroups on \(C_0\)
type: Item
instance of: scholarly article
title: Path regularity for Feller semigroups via Gaussian kernel estimates and generalizations to arbitrary semigroups on \(C_0\)
zbMATH Open document ID: 1080.60038
publication date: 2005-10-28T00:00:00Z
review text: Let \(X_t\) be a Feller process with values in a complete locally compact metric space \(E\). The author gives conditions for the paths of the process \(X_t\) to be locally Hölder continuous or to belong to some weighted Besov spaces. The conditions are formulated in terms of variations of paths for dyadic times \(t=j2^{-n}\), \(j=0,1,\ldots ,2^n\), \(n\in \mathbb N\), and can be reformulated in such a way that they make sense (as a special property) for arbitrary semigroups of operators on \(C_0(E)\). Then it is proved that the above conditions are satisfied if the semigroup satisfies Gaussian kernel estimates typical for Feller semigroups on fractals and for semigroups generated by elliptic operators on \(\mathbb R^d\) of order \(m\geq d\).
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 47D07
zbMATH DE Number: 2220713
zbMATH Keywords: Hölder continuity of paths
zbMATH Keywords: weighted Besov space
author: Sönke Blunck
MaRDI profile type: Publication
full work available at URL: s00440-004-0415-2
OpenAlex ID: W1983624704
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DOI: 10.1007/S00440-004-0415-2
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article