@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 -
Belili, Nacereddine. Dualité du problème des marges et ses applications. Séminaire de probabilités de Strasbourg, Volume 33 (1999), pp. 371-387. http://archive.numdam.org/item/SPS_1999__33__371_0/
[1] Détermination d'un couple optimal du problème de Monge Kantorovich. C. R. Acad. Sci.Paris, 319:981-984, 1994. | MR | Zbl
[2] Sur la distance de deux lois dans le cas vectoriel. C. R. Acad. Sci.Paris, 319:397-400, 1994. | MR | Zbl
, ET[3] Shift-coupling. Stoch. Proc. Appl, 44:1-14, 1993. | MR | Zbl
[4] Large deviations and variational theorem for marginal problems. Preprint, 1996. | MR
, ET .[5] Forme abstraite du théorème de capacitabilité. Ann. Inst. Fourier, 9:83-89, 1959. | EuDML | Numdam | MR | Zbl
[6] Notes on the Wasserstein metric in Hilbert spaces. Ann. Probab., 17:1264-1276, 1989. | MR | Zbl
, AND[7] On lower bounds for the l2-Wasserstein metric in a Hilbert space. J. of Theoretical Prob., 9:263-283, 1996. | MR | Zbl
, , AND .[8] Fréchet classes and compatibility of distribution function. Sym. Math., 9:131-150, 1972. | MR | Zbl
.[9] Probabilités et potentiel. Herman, Paris, 1983. | MR
,[10] Sur le théorème de Hahn-Banach. Rev. Sci, 79:642-643, 1941. | JFM | MR | Zbl
[11] 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] The Fréchet distance between multivariate normal distribution. J. Multivariate Anal., 12:450-455, 1982. | MR | Zbl
,[13] Distances of probability measures and random variables. Ann. Math. Stat., 39:1563-1572, 1968. | MR | Zbl
[14] Probability and metrics. Aarhus Univ., Aarhus, 1976.
[15] Real analysis and probability. Chapman and Hall, New York London, 1989. | Zbl
[16] Linear Operators. Interscience Publishers, a division of John Wiley and Sons, New York, t. I, 1958. | MR | Zbl
, AND[17] On the existence of probability measures with given marginals. Ann. Inst. Fourier., 28:53-78, 1978. | Numdam | MR | Zbl
[18] Sur le théorème de Kantorovitch-Rubinstein dans les espaces polonais. Lecture Notes in Mathematics 850., Springer, 1981. | Numdam | MR | Zbl
[19] Sur les tableaux de corrélation dont les marges sont données. Annales de l'université de Lyon, Sciences., 4:13-84, 1951. | Zbl
[20] Sur la distance de deux lois de probabilité. C. R. Acad. Sci.Paris., 244,1957. | MR | Zbl
[21] The geometry of optimal transportation. Acta. Math., 177:113-161, 1996. | MR | Zbl
, AND[22] On a formula for the l2-Wasserstein metric between measures on Euclidean and Hilbert spaces. Math. Nachr., 147:185-203, 1990. | MR | Zbl
.[23] A class of Wasserstein metrics for probability distributions. Michigan Math. J., 31:231-240, 1984. | MR | Zbl
, AND[24] Maximal coupling. Z. Wahrscheinlichkeitstheor. Verw. Geb., 46:193-204, 1979. | MR | Zbl
[25] A maximal coupling for Markov chains. Z. Wahrscheinlichkeitstheor. Verw. Geb., 31:95-106, 1975. | MR | Zbl
[26] Uniform coupling of non-homogenous Markov chains. J. Appl. Probability, 12:753-762, 1975. | MR | Zbl
[27] Monte Carlo methods. Meth, London,1964. | Zbl
, AND[28] Mesures marginales et théorème de Ford-Fulkerson. Z. Wahrscheinlichkeitstheor. Verw. Geb., 43:245-251, 1978. | MR | Zbl
, AND[29] Functional Analysis and Time optimal control. Academic Press, New York and London, 1969. | MR | Zbl
, AND[30] Stochastic inequalities on partially ordered spaces. Ann. Probab., 5:899-912, 1977. | MR | Zbl
, AND .[31] On the translocation of masses. C. R. (Doklady) Acad. Sci. URSS (N.S.), 37:199-201, 1942. | MR | Zbl
[32] On a problem of Monge (in russian). Uspekhi Math. Nauk, 3:225-226, 1948.
[33] Duality theorems for marginal problems. Z. Wahrscheinlichkeitstheor. Verw. Geb., 67:399-432,1984. | MR | Zbl
[34] Linear topological spaces. D. Van Nostrand Company, Princeton, N. I, 1963. | MR | Zbl
, AND[35] On the optimal mapping of distributions. J. Optim. Th. Appl., 43:39-49, 1984. | MR | Zbl
, AND[36] Lectures on the coupling method. Wiley, New York, 1993. | MR | Zbl
[37] On the invariance principle for sums of independent identically distributed random variables. J. Multivariate Anal., 8:487-517, 1978. | MR | Zbl
[38] Inequalities theory of majorization and its applications. Academic Press, New York, 1979. | MR | Zbl
,[39] 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] The distance between two random vectors with given dispertion matrices. Linear Algebra Appl., 48:257-263, 1982. | MR | Zbl
, AND[41] On coupling of Markov chains. Z. Wahrscheinlichkeitstheor. Verw. Geb., 35:315-322, 1976. | MR | Zbl
[42] The Monge Kantorovich mass transference problem and its stochastic applications. Theory Prob. Appl., 29:647-676, 1984. | MR | Zbl
[43] On a problem of Dudley. Soviet. Math. Dokl., 29:162-164, 1984. | MR | Zbl
[44] Probability metrics and the stability of the stochastic models. Wiley, New York, 1991. | MR | Zbl
[45] Uniformities for the convergence in law and in probability. J. of Theoretical Prob., 5:33-44, 1992. | MR | Zbl
, , AND[46] A general duality theorem for marginal problems. Probab. Theory Relat. Fields, 101:311-319, 1995. | MR | Zbl
, AND[47] Duality and perfect probability spaces. Proceedings of the American mathematical society, 124:2223-2228, 1996. | MR | Zbl
, AND[48] Convex Analysis. Princeton, Univ. Press, 1970. | MR | Zbl
[49] 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] A characterization of random variables with minimum l2-distance. J. of Multivariate Anal., 32:48-54, 1990. | MR | Zbl
, AND[51] The existence of probability measures with given marginals. Ann. Probab., 21:136-142, 1993. | MR | Zbl
[52] Antithetic variates for Monte-Carlo estimation of probabilities. Statistics Neerlandica, 38:1-19, 1984. | MR | Zbl
[53] The existence of measures with given marginals. Ann. Math. Stat, 36:423-439, 1965. | MR | Zbl
[54] On minimal metrics in the space of random variables. Theory Prob. Appl., 27:424-430, 1982. | MR | Zbl
[55] On maximal and distributional coupling. Ann. Probab., 14:873-876, 1986. | MR | Zbl
[56] Calculation of the Wasserstein distance between probability distributions on the line. Theory. Prob. Appl., 18:784-786, 1973. | Zbl