Title
Distances on probability measures and random variables Distances on probability measures and random variables
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Journal of mathematical analysis and applications. - New York, N.Y.
Volume/pages
374(2011) :2 , p. 412-428
ISSN
0022-247X
ISI
000283965000007
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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.
E-info
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