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Erschienen in:
Main Directions in the Theory of Probability Metrics Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

5. Monge–Kantorovich Mass Transference Problem, Minimal Distances and Minimal Norms

verfasst von : Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

Erschienen in: The Methods of Distances in the Theory of Probability and Statistics

Verlag: Springer New York

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Abstract

The goals of this chapter are to: Introduce the Kantorovich and Kantorovich–Rubinstein problems in one-dimensional and multidimensional settings; Provide examples illustrating applications of the abstract problems; Provide examples illustrating applications of the abstract problems; Discuss the multivariate Kantorovich and Kantorovich–Rubinstein theorems, which provide dual representations of certain types of minimal distances and norms; Discuss a particular application leading to an explicit representation for a class of minimal norms.

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Vorheriges Kapitel A Structural Classification of Probability Distances
Nächstes Kapitel Quantitative Relationships Between Minimal Distances and Minimal Norms
Fußnoten
1
The program of the conference and related materials are available online at http://​www.​mccme.​ru/​%5C~ansobol/​otarie/​MK2012conf.​html.
 
2
See Rachev [1991], Rachev and Taksar [1992], Rachev and Hanin [1995a,b], Cuesta et al. [1996], and Rachev and Rüschendorf [1999].
 
3
See, for example, Bazaraa and Jarvis [2005].
 
4
See also the general discussion in Whittle (1982, p. 210–211).
 
5
See Gray (1988, p. 48).
 
6
See Kalashnikov and Rachev [1988, Chaps.​ 3 and 6].
 
7
See, for example, Bazaraa and Jarvis [2005].
 
8
See Bazaraa and Jarvis [2005] and Berge and Chouila-Houri [1965, Sect. 9.8].
 
9
See Fortet and Mourier [1953].
 
10
See Dunford and Schwartz [1988, p. 65].
 
11
See also Dudley [2002, Theorem 11.6.2].
 
12
See Sect. 2.2 of Chap.​ 2.
 
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Metadaten
Titel
Monge–Kantorovich Mass Transference Problem, Minimal Distances and Minimal Norms
verfasst von
Svetlozar T. Rachev
Lev B. Klebanov
Stoyan V. Stoyanov
Frank J. Fabozzi
Copyright-Jahr
2013
Verlag
Springer New York
Buch
The Methods of Distances in the Theory of Probability and Statistics

Print ISBN: 978-1-4614-4868-6

Electronic ISBN: 978-1-4614-4869-3

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-1-4614-4869-3_5