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Mass transportation problems with capacity constraints

Part of: Distribution theory - Probability Multivariate analysis Distribution theory

Published online by Cambridge University Press:  14 July 2016

S. T. Rachev  and
I. Olkin
S. T. Rachev*
Affiliation:
University of California, Santa Barbara
I. Olkin*
Affiliation:
Stanford University
*
∗Postal address: Statistics and Applied Probability, University of California, Santa Barbara, CA 93106–3110, USA.
∗∗Postal address: Department of Statistics, Stanford University, Stanford, CA 94305–4065, USA. Supported in part by National Science Foundation.
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Abstract

We exhibit solutions of Monge–Kantorovich mass transportation problems with constraints on the support of the feasible transportation plans and additional capacity restrictions. The Hoeffding–Fréchet inequalities are extended for bivariate distribution functions having fixed marginal distributions and satisfying additional constraints. Sharp bounds for different probabilistic functionals (e.g. Lp-distances, covariances, etc.) are given when the family of joint distribution functions has prescribed marginal distributions, satisfies restrictions on the support, and is bounded from above, or below, by other distributions.

Keywords

Monge–Kantorovich problemmultivariate distributionsmarginal distributionsmeasures of dependencelinear programminggreedy algorithms

MSC classification

Primary: 60E05: Distributions 62E10: Characterization and structure theory
Secondary: 62H05: Characterization and structure theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 433 - 445
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

Supported in part by Econometric Institute, Erasmus University, Rotterdam and the Alexander von Humboldt Foundation.

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