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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Published in | Journal of mathematical analysis and applications Vol. 384; no. 1; pp. 33 - 48 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.12.2011
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0022-247X 1096-0813 |
DOI: | 10.1016/j.jmaa.2011.03.014 |