非扇形Dirichlet型的拟正则性
On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets
摘要：
得到了广义（非扇形）Dirichlet型的拟正则性的一个判别准则，推广了P.J.Fitzsimmons关于（扇形）半Dirichlet型的拟正则性的结果.给定与半狄利克雷型相关联的右（马尔可夫）过程，我们给出了第二个右过程是标准右过程且具有相同状态空间的充分条件.上述的拟正则性准则就是一个应用。条件表示在相关的能力，紧套，极集，和准连续性。第二个应用是关于拟正则性的广义狄利克雷形式扰动半狄利克雷形式与核。
英文摘要：
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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