Weak convergence of symmetric diffusion processes

Summary. In this paper, we show the convergence of forms in the sense of Mosco associated with the part form on relatively compact open set of Dirichlet forms with locally uniform ellipticity and the locally uniform boundedness of ground states under regular Dirichlet space setting. We also get the same assertion under Dirichlet space in infinite dimensional setting. As a result of this, we get the weak convergence under some conditions on initial distributions and the growth order of the volume of the balls defined by (modified) pseudo metric used in K. Th. Sturm. Received: 18 September 1995 / In revised form: 23 January 1997