A Transformation of Dirichlet Forms and Its Related Markov Process

In this paper, we study a transformation of Dirichlet forms. We obtain the sufficient conditions ensuring the transformed bilinear forms is quasi-regular Dirichlet forms. We separately study about the Dirichlet form for a type of second order differential operator and jump measure, and obtain the relationship between the Markov processes which is corresponding to quasi-regular Dirichlet type before and after the transformation.