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Alexander V. Kolesnikov

Convergence of Dirichlet forms with changing speed measures on ?^d

We consider a sequence of vaguely convergent measures ?_n = ?_n dx ? ? dx = ? on ?^d and a sequence of symmetric Dirichlet forms {?_n}, ?_n(f, g) = ?^d_i,j=1 ?_?d aⁿ_i,j?_i f ?_j g dx, where every ? _n is defined on L²(?_n 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 {?_n} and weak convergence of finite dimensional distributions of associated stochastic processes.

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 17, 03/2005
Pages: 225 - 259

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