Weak convergence of diffusion processes on Wiener space |
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Authors: | Alexander V. Kolesnikov |
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Affiliation: | (1) Scuola Normale Superiore, Centro Di Ricerca Matematica Ennio De Giorgi, 56100 Pisa, Italy |
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Abstract: | Let γ be a Gaussian measure on a Suslin space X, H be the corresponding Cameron–Martin space and {e i } ⊂ H be an orthonormal basis of H. Suppose that μ n = ρ n · γ is a sequence of probability measures which converges weakly to a probability measure μ = ρ · γ Consider a sequence of Dirichlet forms , where and . We prove some sufficient conditions for Mosco convergence where . In particular, if X is a Hilbert space, and can be uniformly approximated by finite dimensional conditional expectations for every fixed e i , then under broad assumptions Mosco and the distributions of the associated stochastic processes converge weakly. |
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Keywords: | Dirichlet forms Mosco convergence Convergence of stochastic processes Gaussian measures |
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