Quasi - Canonicality Of A Class Of Dirichlet Type In Wiener Space

The quasi-regularity of Dirichlet forms plays a very important role in the construc-tion of Markov processes on infinite dimensional spaces. This paper mainly proves the closability and quasi-regularity of a class of Dirichlet forms. Moreover, the paper ob-tains a comparison theorem about quasi-regularity. Specifically, this paper is organized as follows:Chapter1is a preliminary chapter in which we mainly introduce the background of the problem and our main results.Chapter2mainly introduces basic concepts about Dirichlet forms and Wiener spaces. Moreover, we introduce the definition of quasi-regular Dirichlet forms and the relevant knowledge in detail.Chapter3is a main part of this paper in which we prove the closability and quasi-regularity of a class of Dirichlet forms and then obtain a comparison theorem about quasi-regularity and the relevant comparison theorem on functional inequatities.