On a Laplace Transform Based Metric for Probabilities on a Hilbert Space |
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Authors: | Suman Majumdar |
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Institution: | (1) University of Connecticut, 1 University Place, Stamford, Connecticut, 06901-2315 |
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Abstract: | Let D be a closed subset of a real separable Hilbert space H. Let (D) denote the set of all Borel probability measures on D and (D) the set of all probabilities with integrable Laplace transform. A metric d, based on the Laplace transform, is defined on (D). Topological properties, viz., separability, connectedness, completeness, compactness and local compactness, of (D, d are investigated, and the d-topology is compared with the topology of weak convergence. |
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Keywords: | Characteristic function convolution Laplace transform weak convergence |
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