Convergence of distorted Brownian motions and singular Hamiltonians

摘要: We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms the kind \(\varepsilon _\phi \left( {f,g} \right) = \tfrac{1}{2}\int_{\mathbb{R}^d } {\nabla f} x \cdot \nabla g\left( \right)\phi ^2 \right)dx\).We obtain in total variation norm probability measures on path space C(ℝ+;ℝd) under hypotheses which, example, are satisfied case Hloc1(ℝd)-convergence ϕ's, but we can allow more singular situations as regards approximating sequences. use then these results give criterion generalized Schrodinger operators which potential function should not necessarily exists measurable function. only strong resolvent sense, also uniform operator topology up sets arbitrarily small Lebesgue measure. Applications problem approximation ordinary by ones zero-range interactions given.