Convergence of Dirichlet Forms Induced on Boundaries of Transient Networks

In this paper, the Kuramochi boundary of a connected transient network is studied in connection with the Hilbert space consisting of functions with finite Dirichlet sum, and it is proved that the Dirichlet form induced on the boundary of a connected finite subset of the network Mosco-converges to that on the Kuramochi boundary as the connected finite subset increases to exhaust the network.