Convergence of Dirichlet forms with changing speed measures on ℝ d

Abstract

We consider a sequence of vaguely convergent measures μn = σn dx → σ dx = μ on ℝd and a sequence of symmetric Dirichlet forms {ℰn}, ℰn(f, g) = ∑di,j=1 ∫ℝdani,j∂i f ∂j g dx, where every ℰ n is defined on L2(σn dx). We apply a functional analytic theory of Mosco convergence on changing L2-spaces recently developed by K. Kuwae and T. Shioya and obtain some new results about convergence of {ℰn} and weak convergence of finite dimensional distributions of associated stochastic processes.