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P. Cattiaux (1)
F. Gamboa (2)
|(1)||Ecole Polytechnique, CMAP, F-91128 Palaiseau Cedex, CNRS 756|
Université Paris X Nanterre, equipe MODAL'X, UFR SEGMI, 200 av. de la république, F-91001 Nanterre Cedex.
|(2)||Laboratoire de Statistiques Université Paris Sud F-91405 Orsay|
Université Paris-Nord Institut Galilée F-93430 Villetaneuse.
Abstract : On a product Probability space , we give variational characterizations for the existence of a Probability measure Q with given marginals, such that Q is absolutely continuous with respect to P, and its density satisfies some integrability conditions.
These characterizations, which are in some sense the dual formulation of a Theorem of Strassen , are obtained by using large deviations methods. We also study the minimal realizations of such Q.
Keywoords : Marginal Problems-Large Deviations
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