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Duality theorem for marginal problems and its applications. (Dualité du problème des marges et ses applications.) (French) Zbl 0949.62011

Azéma, Jacques (ed.) et al., Séminaire de probabilités XXXIII. Berlin: Springer. Lect. Notes Math. 1709, 371-387 (1999).
This paper gives in the first part a review on the duality theorem for marginal problems and some of its applications to stochastic order and representation of metrics as minimal metrics, resp. to the calculation of minimal metrics. One should mention in this context that the optimal coupling of distributions w.r.t. convex functions of the form \(\Phi(x-y)\) by quantile transformations should be attributed historically to early papers of Hoeffding, Dall Aglio, Fréchet and Bertino.
In the second part, a direct proof is given for the Goldstein theorem on maximal coupling based on a well known theorem on measures which concentrate maximally on the diagonal.
For the entire collection see [Zbl 0924.00016].

MSC:

62E10 Characterization and structure theory of statistical distributions
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