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Title
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Distances on probability measures and random variables
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Author
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Abstract
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| In this paper we lift fundamental topological structures on probability measures and random variables, in particular the weak topology, convergence in law and finite-dimensional convergence to an isometric level. This allows for an isometric quantitative study of important concepts such as relative compactness, tightness, stochastic equicontinuity, Prohorov's theorem and σ-smoothness. In doing so we obtain numerical results which allow for the development of an intrinsic approximation theory and from which moreover all classical topological results follow as easy corollaries. |
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Language
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English
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Source (journal)
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Journal of mathematical analysis and applications. - New York, N.Y.
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Publication
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New York, N.Y.
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2011
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ISSN
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0022-247X
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DOI
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10.1016/J.JMAA.2010.09.006
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Volume/pages
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374
:2
(2011)
, p. 412-428
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ISI
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000283965000007
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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