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

Lucian Beznea; Gerald Trutnau

doi:10.1016/j.jmaa.2011.03.014

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arXiv · 1012.2227

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

Lucian Beznea·Gerald Trutnau

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Abstract

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. A 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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Lucian Beznea, Gerald Trutnau. 2010-12-10. On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets. https://doi.org/10.1016/j.jmaa.2011.03.014

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