Dualité du problème des marges et ses applications
Séminaire de probabilités de Strasbourg, Tome 33 (1999), pp. 371-387.
@article{SPS_1999__33__371_0,
     author = {Belili, Nacereddine},
     title = {Dualit\'e du probl\`eme des marges et ses applications},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     pages = {371--387},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {33},
     year = {1999},
     mrnumber = {1768011},
     zbl = {0949.62011},
     language = {fr},
     url = {http://archive.numdam.org/item/SPS_1999__33__371_0/}
}
TY  - JOUR
AU  - Belili, Nacereddine
TI  - Dualité du problème des marges et ses applications
JO  - Séminaire de probabilités de Strasbourg
PY  - 1999
SP  - 371
EP  - 387
VL  - 33
PB  - Springer - Lecture Notes in Mathematics
UR  - http://archive.numdam.org/item/SPS_1999__33__371_0/
LA  - fr
ID  - SPS_1999__33__371_0
ER  - 
%0 Journal Article
%A Belili, Nacereddine
%T Dualité du problème des marges et ses applications
%J Séminaire de probabilités de Strasbourg
%D 1999
%P 371-387
%V 33
%I Springer - Lecture Notes in Mathematics
%U http://archive.numdam.org/item/SPS_1999__33__371_0/
%G fr
%F SPS_1999__33__371_0
Belili, Nacereddine. Dualité du problème des marges et ses applications. Séminaire de probabilités de Strasbourg, Tome 33 (1999), pp. 371-387. http://archive.numdam.org/item/SPS_1999__33__371_0/

[1] Abdellaoui, T. Détermination d'un couple optimal du problème de Monge Kantorovich. C. R. Acad. Sci.Paris, 319:981-984, 1994. | MR | Zbl

[2] Abdellaoui, T., ET Heinich, H. Sur la distance de deux lois dans le cas vectoriel. C. R. Acad. Sci.Paris, 319:397-400, 1994. | MR | Zbl

[3] Aldous, D.J. Shift-coupling. Stoch. Proc. Appl, 44:1-14, 1993. | MR | Zbl

[4] Cattiaux, P., ET F. Gamboa. Large deviations and variational theorem for marginal problems. Preprint, 1996. | MR

[5] Choquet, G. Forme abstraite du théorème de capacitabilité. Ann. Inst. Fourier, 9:83-89, 1959. | EuDML | Numdam | MR | Zbl

[6] Cuesta-Albertos, J.A., AND Matrán, C. Notes on the Wasserstein metric in Hilbert spaces. Ann. Probab., 17:1264-1276, 1989. | MR | Zbl

[7] Cuesta-Albertos, J.A., Matrán, C., AND Tuero-Diaz, A. . On lower bounds for the l2-Wasserstein metric in a Hilbert space. J. of Theoretical Prob., 9:263-283, 1996. | MR | Zbl

[8] Dall'Aglio. Fréchet classes and compatibility of distribution function. Sym. Math., 9:131-150, 1972. | MR | Zbl

[9] Dellacherie, C., Meyer, P.A. Probabilités et potentiel. Herman, Paris, 1983. | MR

[10] Dieudonné, J. Sur le théorème de Hahn-Banach. Rev. Sci, 79:642-643, 1941. | JFM | MR | Zbl

[11] Doeblin, W. Exposé de la théorie des chaînes simples constantes de Markov à un nombre fini d'états. Rev. Math. Union Interbalkanique, 2:77-105, 1938. | JFM | Zbl

[12] Dowson, D.C., Landau, B.V. The Fréchet distance between multivariate normal distribution. J. Multivariate Anal., 12:450-455, 1982. | MR | Zbl

[13] Dudley, R.M. Distances of probability measures and random variables. Ann. Math. Stat., 39:1563-1572, 1968. | MR | Zbl

[14] Dudley, R.M. Probability and metrics. Aarhus Univ., Aarhus, 1976.

[15] Dudley, R.M. Real analysis and probability. Chapman and Hall, New York London, 1989. | Zbl

[16] Dunford, N., AND Schwartz, J.T. Linear Operators. Interscience Publishers, a division of John Wiley and Sons, New York, t. I, 1958. | MR | Zbl

[17] Edwards, D.A. On the existence of probability measures with given marginals. Ann. Inst. Fourier., 28:53-78, 1978. | Numdam | MR | Zbl

[18] Fernique, X. Sur le théorème de Kantorovitch-Rubinstein dans les espaces polonais. Lecture Notes in Mathematics 850., Springer, 1981. | Numdam | MR | Zbl

[19] Fréchet, M. Sur les tableaux de corrélation dont les marges sont données. Annales de l'université de Lyon, Sciences., 4:13-84, 1951. | Zbl

[20] Fréchet, M. Sur la distance de deux lois de probabilité. C. R. Acad. Sci.Paris., 244,1957. | MR | Zbl

[21] Gangbo, W., AND Mccann, R.J. The geometry of optimal transportation. Acta. Math., 177:113-161, 1996. | MR | Zbl

[22] Gelbrich, M.. On a formula for the l2-Wasserstein metric between measures on Euclidean and Hilbert spaces. Math. Nachr., 147:185-203, 1990. | MR | Zbl

[23] Givens, C.R., AND Shortt, R.M. A class of Wasserstein metrics for probability distributions. Michigan Math. J., 31:231-240, 1984. | MR | Zbl

[24] Goldstein, S. Maximal coupling. Z. Wahrscheinlichkeitstheor. Verw. Geb., 46:193-204, 1979. | MR | Zbl

[25] Griffeath, D. A maximal coupling for Markov chains. Z. Wahrscheinlichkeitstheor. Verw. Geb., 31:95-106, 1975. | MR | Zbl

[26] Griffeath, D. Uniform coupling of non-homogenous Markov chains. J. Appl. Probability, 12:753-762, 1975. | MR | Zbl

[27] Hammersley, I.M., AND Handscomb, D.C. Monte Carlo methods. Meth, London,1964. | Zbl

[28] Hansel, G., AND Troallic, J.P. Mesures marginales et théorème de Ford-Fulkerson. Z. Wahrscheinlichkeitstheor. Verw. Geb., 43:245-251, 1978. | MR | Zbl

[29] Hermes, H., AND Lasalle, J.P. Functional Analysis and Time optimal control. Academic Press, New York and London, 1969. | MR | Zbl

[30] Kamae, T., Krengel, U. AND O'Brien. Stochastic inequalities on partially ordered spaces. Ann. Probab., 5:899-912, 1977. | MR | Zbl

[31] Kantorovich, L.V. On the translocation of masses. C. R. (Doklady) Acad. Sci. URSS (N.S.), 37:199-201, 1942. | MR | Zbl

[32] Kantorovich, L.V. On a problem of Monge (in russian). Uspekhi Math. Nauk, 3:225-226, 1948.

[33] Kellerer, H.G. Duality theorems for marginal problems. Z. Wahrscheinlichkeitstheor. Verw. Geb., 67:399-432,1984. | MR | Zbl

[34] Kelley, J.L., AND Namioka, I. Linear topological spaces. D. Van Nostrand Company, Princeton, N. I, 1963. | MR | Zbl

[35] Knott, M., AND Smith, C.S. On the optimal mapping of distributions. J. Optim. Th. Appl., 43:39-49, 1984. | MR | Zbl

[36] Lindvall, T. Lectures on the coupling method. Wiley, New York, 1993. | MR | Zbl

[37] Major, P. On the invariance principle for sums of independent identically distributed random variables. J. Multivariate Anal., 8:487-517, 1978. | MR | Zbl

[38] Marshall, A.W., Olkin, I. Inequalities theory of majorization and its applications. Academic Press, New York, 1979. | MR | Zbl

[39] Monge, G. Mémoire sur la théorie des déblais et des remblais. Histoires de l'Académie Royale des Sciences de Paris, avec les mémoires de Mathématiques et de Physique pour la même année, pages 257-263, 1781.

[40] Olkin, I., AND Pukelsheim, F. The distance between two random vectors with given dispertion matrices. Linear Algebra Appl., 48:257-263, 1982. | MR | Zbl

[41] Pitman, J.W. On coupling of Markov chains. Z. Wahrscheinlichkeitstheor. Verw. Geb., 35:315-322, 1976. | MR | Zbl

[42] Rachev, S.T. The Monge Kantorovich mass transference problem and its stochastic applications. Theory Prob. Appl., 29:647-676, 1984. | MR | Zbl

[43] Rachev, S.T. On a problem of Dudley. Soviet. Math. Dokl., 29:162-164, 1984. | MR | Zbl

[44] Rachev, S.T. Probability metrics and the stability of the stochastic models. Wiley, New York, 1991. | MR | Zbl

[45] Rachev, S.T., Rüschendorf, L., AND Schief, A. Uniformities for the convergence in law and in probability. J. of Theoretical Prob., 5:33-44, 1992. | MR | Zbl

[46] Ramachandran, D., AND Rüschendorf, L. A general duality theorem for marginal problems. Probab. Theory Relat. Fields, 101:311-319, 1995. | MR | Zbl

[47] Ramachandran, D., AND Rüschendorf, L. Duality and perfect probability spaces. Proceedings of the American mathematical society, 124:2223-2228, 1996. | MR | Zbl

[48] Rockafellar, R.T. Convex Analysis. Princeton, Univ. Press, 1970. | MR | Zbl

[49] Rüschendorf, L. Fréchet bounds and their applications. In Kotz S Dall'Aglio, G. and Salinetti G, editors, Advances in probability distributions with given marginals: Beyond the Copulas, pages 141-176. Dordrecht, Kluwer Academic Publishers, 1991. | MR | Zbl

[50] Rüschendorf, L., AND Rachev, S. A characterization of random variables with minimum l2-distance. J. of Multivariate Anal., 32:48-54, 1990. | MR | Zbl

[51] Skala, H.G. The existence of probability measures with given marginals. Ann. Probab., 21:136-142, 1993. | MR | Zbl

[52] Snijders, T.A.B. Antithetic variates for Monte-Carlo estimation of probabilities. Statistics Neerlandica, 38:1-19, 1984. | MR | Zbl

[53] Strassen, V. The existence of measures with given marginals. Ann. Math. Stat, 36:423-439, 1965. | MR | Zbl

[54] Szugla, A. On minimal metrics in the space of random variables. Theory Prob. Appl., 27:424-430, 1982. | MR | Zbl

[55] Thorisson, H. On maximal and distributional coupling. Ann. Probab., 14:873-876, 1986. | MR | Zbl

[56] Vallender, S.S. Calculation of the Wasserstein distance between probability distributions on the line. Theory. Prob. Appl., 18:784-786, 1973. | Zbl