On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets

We obtain a criterion for the quasi-regularity of generalized (non-sectorial) Dirichlet forms, which extends the result of P.J. Fitzsimmons on the quasi-regularity of (sectorial) semi-Dirichlet forms. Given the right (Markov) process associated to a semi-Dirichlet form, we present sufficient conditi...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 384; no. 1; pp. 33 - 48
Main Authors Beznea, Lucian, Trutnau, Gerald
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2011
Subjects
Capacity
Dirichlet form
Generalized Dirichlet form
Polar set
Quasi-continuity
Quasi-regularity
Right process
Standard process
Weak duality
Standard process
Polar set
Capacity
Dirichlet form
Quasi-continuity
Weak duality
Right process
Generalized Dirichlet form
Quasi-regularity
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Summary:We obtain a criterion for the quasi-regularity of generalized (non-sectorial) Dirichlet forms, which extends the result of P.J. Fitzsimmons on the quasi-regularity of (sectorial) semi-Dirichlet forms. Given the right (Markov) process associated to a semi-Dirichlet form, we present sufficient conditions for a second right process to be a standard one, having the same state space. The above mentioned quasi-regularity criterion is then an application. The conditions are expressed in terms of the associated capacities, nests of compacts, polar sets, and quasi-continuity. The second application is on the quasi-regularity of the generalized Dirichlet forms obtained by perturbing a semi-Dirichlet form with kernels.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.03.014