Mass Transportation Problems: Volume I: Theory
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1998
|
| Schriftenreihe: | Probability and its Applications, A Series of the Applied Probability Trust
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1.1 Mass Transportation Problems in Probability Theory This chapter provides a basic introduction to mass transportation pr- lems (MTPs). We introduce some of the methods used in studying MTPs: dualrepresentations,explicitsolutions,topologicalproperties.Weshallalso discuss some applications of MTPs. The following measure-theoretic problems are well-known continuous casesofMKPs(see,forexample,Dudley(1976),LevinandMilyutin(1979), R¨ uschendorf (1979, 1981), Kemperman (1983), Kellerer (1984), Rachev (1984b, 1991c) and the references therein). TheMonge–Kantorovichmasstransportationproblem(MKP):Given?xed probability measuresP andP on a separable metric spaceS and a mea- 1 2 surable cost functionc on the Cartesian productS×S, ?nd µ (P,P ) = inf c(x,y)P(dx, dy), (1.1.1) c 1 2 wherethein?mumistakenoverallprobabilitymeasuresP onS×S having projections ?P = P,i=1,2. (1.1.2) i i 2 1. Introduction The Kantorovich–Rubinstein transshipment problem (KRP): GivenP 1 andP onS ?nd 2 ? µ (P,P ) = inf c(x,y)Q(dx, dy), (1.1.3) 1 2 c where the in?mum is taken over all ?nite measuresQ onS×S having the marginal di?erence ?Q??Q = P ?P ; (1.1.4) 1 2 1 2 that is,Q(A×S)?Q(S×A)=P (A)?P (A) for all Borel setsA?S. |
| Beschreibung: | 1 Online-Ressource (XXVI, 508 p) |
| ISBN: | 9780387227559 9780387983509 |
| ISSN: | 1431-7028 |
| DOI: | 10.1007/b98893 |
Internformat
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/b98893 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780387227559 9780387983509 |
| issn | 1431-7028 |
| language | English |
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| spelling | Rachev, Svetlozar T. Verfasser aut Mass Transportation Problems Volume I: Theory by Svetlozar T. Rachev, Ludger Rüschendorf New York, NY Springer New York 1998 1 Online-Ressource (XXVI, 508 p) txt rdacontent c rdamedia cr rdacarrier Probability and its Applications, A Series of the Applied Probability Trust 1431-7028 1.1 Mass Transportation Problems in Probability Theory This chapter provides a basic introduction to mass transportation pr- lems (MTPs). We introduce some of the methods used in studying MTPs: dualrepresentations,explicitsolutions,topologicalproperties.Weshallalso discuss some applications of MTPs. The following measure-theoretic problems are well-known continuous casesofMKPs(see,forexample,Dudley(1976),LevinandMilyutin(1979), R¨ uschendorf (1979, 1981), Kemperman (1983), Kellerer (1984), Rachev (1984b, 1991c) and the references therein). TheMonge–Kantorovichmasstransportationproblem(MKP):Given?xed probability measuresP andP on a separable metric spaceS and a mea- 1 2 surable cost functionc on the Cartesian productS×S, ?nd µ (P,P ) = inf c(x,y)P(dx, dy), (1.1.1) c 1 2 wherethein?mumistakenoverallprobabilitymeasuresP onS×S having projections ?P = P,i=1,2. (1.1.2) i i 2 1. Introduction The Kantorovich–Rubinstein transshipment problem (KRP): GivenP 1 andP onS ?nd 2 ? µ (P,P ) = inf c(x,y)Q(dx, dy), (1.1.3) 1 2 c where the in?mum is taken over all ?nite measuresQ onS×S having the marginal di?erence ?Q??Q = P ?P ; (1.1.4) 1 2 1 2 that is,Q(A×S)?Q(S×A)=P (A)?P (A) for all Borel setsA?S. Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Rüschendorf, Ludger Sonstige oth https://doi.org/10.1007/b98893 Verlag Volltext |
| spellingShingle | Rachev, Svetlozar T. Mass Transportation Problems Volume I: Theory Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik |
| title | Mass Transportation Problems Volume I: Theory |
| title_auth | Mass Transportation Problems Volume I: Theory |
| title_exact_search | Mass Transportation Problems Volume I: Theory |
| title_full | Mass Transportation Problems Volume I: Theory by Svetlozar T. Rachev, Ludger Rüschendorf |
| title_fullStr | Mass Transportation Problems Volume I: Theory by Svetlozar T. Rachev, Ludger Rüschendorf |
| title_full_unstemmed | Mass Transportation Problems Volume I: Theory by Svetlozar T. Rachev, Ludger Rüschendorf |
| title_short | Mass Transportation Problems |
| title_sort | mass transportation problems volume i theory |
| title_sub | Volume I: Theory |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik |
| url | https://doi.org/10.1007/b98893 |
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