On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets
type: Item
instance of: scholarly article
title: On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets
zbMATH Open document ID: 1229.60090
author: Lucian Beznea
author: Gerald Trutnau
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-09-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1012.2227
review text: The main result gives sufficient conditions which ensure that the property of being standard is transferred from a right Markov process to a second one, on the same state space. The conditions are expressed in terms of the associated capacities, nests of compacts, polar sets, and quasi-continuity. The first application of this result is the extension of a quasi-regularity criterion due to \textit{P. J. Fitzsimmons} [Potential Anal. 15, No.~3, 151--185 (2001; Zbl 0993.60075)] to the framework of generalized (i.e., non-sectorial) Dirichlet forms, as developed by \textit{W. Stannat} [``The theory of generalized Dirichlet forms and its applications in analysis and stochastics'', Mem. Am. Math. Soc. 678 (1999; Zbl 1230.60006)]. The second application is to the quasi-regularity of the generalized Dirichlet forms obtained by perturbing a semi-Dirichlet form with kernels.
reviewed by: Liliana Popa
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 47D07
zbMATH DE Number: 5947107
zbMATH Keywords: Dirichlet form
zbMATH Keywords: generalized Dirichlet form
zbMATH Keywords: quasi-regularity
zbMATH Keywords: standard process
zbMATH Keywords: capacity
zbMATH Keywords: quasi-continuity
zbMATH Keywords: polar set
zbMATH Keywords: right process
zbMATH Keywords: weak duality
MaRDI profile type: Publication
OpenAlex ID: W2134651724
arXiv ID: 1012.2227
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DOI: 10.1016/J.JMAA.2011.03.014
description: scientific article