  Convergence is proved for solutions of Dirichlet problems in regions with
many small excluded sets (holes), as the holes become smaller and more
numerous. The problem is formulated in the context of Markov processes
associated with general Dirichlet forms, for random and nonrandom excluded
sets. Sufficient conditions are given under which the sequence of entrance
times or hitting times of the excluded sets converges in the stable topology.
Convergence in the stable topology is a strengthened form of convergence in
distribution, introduced by Renyi. Stable convergence of the entrance times
implies convergence of the solutions of the corresponding Dirichlet problems.
Some additional results are given in a supplement on random center models.
