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