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Статья

Convergence of Dirichlet forms with changing speed measures on $\R^d$

Forum Mathematicum. 2005. No. 17. P. 225-259.

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 ∫ℝ d ani,j∂i f ∂j g dx, where every ℰ n is defined on L 2(σn dx). We apply a functional analytic theory of Mosco convergence on changing L 2-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.