EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 16 (2012) ESAIM: PS, 16 (2012) 306-323 References
Free Access
Issue
ESAIM: PS
Volume 16, 2012
Page(s) 306 - 323
DOI https://doi.org/10.1051/ps/2011163
Published online 16 July 2012
  1. J. Aaronson, An introduction to infinite ergodic theory, in Math. Surveys Monogr., Amer. Math. Soc. Providence, RI 50 (1997). [Google Scholar]
  2. J. Aaronson and M. Keane, The visits to zero of some deterministic random walks. Proc. London Math. Soc. 44 (1982) 535–553. [CrossRef] [MathSciNet] [Google Scholar]
  3. L. Ambrosio and A. Pratelli, Existence and stability results in the L1-theory of optimal transportation, CIME Course Lect. Notes Math. 1813 (2003) 123–160. [CrossRef] [Google Scholar]
  4. M. Beiglböck, M. Goldstern, G. Maresh and W. Schachermayer, Optimal and better transport plans. J. Funct. Anal. 256 (2009) 1907–1927. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Beiglböck, C. Léonard and W. Schachermayer, A general duality theorem for the Monge–Kantorovich transport problem. Submitted (2009). [Google Scholar]
  6. M. Beiglböck, C. Léonard and W. Schachermayer, On the duality of the Monge–Kantorovich transport problem, in Summer school on optimal transport. Séminaires et Congrès, Société Mathématique de France, Institut Fourier, Grenoble (2009) [Google Scholar]
  7. Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. 44 (1991) 375–417. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  8. M. Beiglböck and W. Schachermayer, Duality for Borel measurable cost functions. Trans. Amer. Math. Soc. 363 (2011) 4203–4224. [CrossRef] [MathSciNet] [Google Scholar]
  9. Probabilités, I (Univ. Rennes, Rennes, 1976). Exp. No. 5, Dépt. Math. Informat., Univ. Rennes, Rennes (1976) 7. [Google Scholar]
  10. L. Cafarelli and R.J. McCann, Free boundaries in optimal transport and Monge–Ampere obstacle problems. Ann. of Math. 171 (2010) 673–730. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. de Acosta, Invariance principles in probability for triangular arrays of B-valued random vectors and some applications. Ann. Probab. 10 (1982) 346–373. [CrossRef] [MathSciNet] [Google Scholar]
  12. L. Decreusefond, Wasserstein distance on configuration space. Potential Anal. 28 (2008) 283–300. [CrossRef] [MathSciNet] [Google Scholar]
  13. L. Decreusefond, A. Joulin and N. Savy, Upper bounds on Rubinstein distances on configuration spaces and applications. Commun. Stochastic Anal. 4 (2010) 377–399. [Google Scholar]
  14. R.M. Dudley, Probabilities and metrics, Convergence of laws on metric spaces, with a view to statistical testing, No. 45. Matematisk Institut, Aarhus Universitet, Aarhus. Lect. Notes Ser. (1976). [Google Scholar]
  15. R.M. Dudley, Real analysis and probability, Cambridge University Press, Cambridge. Cambridge Studies in Adv. Math. 74 (2002). Revised reprint of the 1989 original. [Google Scholar]
  16. X. Fernique, Sur le théorème de Kantorovich-Rubinstein dans les espaces polonais in Seminar on Probability, XV (Univ. Strasbourg, Strasbourg, 1979/1980) (French). Lect. Notes Math. 850 (1981) 6–10. [CrossRef] [Google Scholar]
  17. A. Figalli, The optimal partial transport problem. Arch. Rational Mech. Anal. 195 (2010) 533–560. [CrossRef] [MathSciNet] [Google Scholar]
  18. D. Feyel and A.S. Üstünel, Measure transport on Wiener space and the Girsanov theorem. C. R. Math. Acad. Sci. Paris 334 (2002) 1025–1028. [CrossRef] [MathSciNet] [Google Scholar]
  19. D. Feyel and A.S. Üstünel, Monge-Kantorovitch measure transportation and Monge–Ampère equation on Wiener space. Probab. Theory Relat. Fields 128 (2004) 347–385. [CrossRef] [Google Scholar]
  20. D. Feyel and A.S. Üstünel, Monge-Kantorovitch measure transportation, Monge–Ampère equation and the Itô calculus, in Stochastic analysis and related topics in Kyoto. Adv. Stud. Pure Math. Math. Soc. Japan 41 (2004) 49–74. [Google Scholar]
  21. D. Feyel and A.S. Üstünel, Solution of the Monge-Ampère equation on Wiener space for general log-concave measures. J. Funct. Anal. 232 (2006) 29–55. [CrossRef] [MathSciNet] [Google Scholar]
  22. N. Gaffke and L. Rüschendorf, On a class of extremal problems in statistics. Math. Operationsforsch. Statist. Ser. Optim. 12 (1981) 123–135. [CrossRef] [MathSciNet] [Google Scholar]
  23. W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math. 177 (1996) 113–161. [CrossRef] [MathSciNet] [Google Scholar]
  24. L.V. Kantorovich, On the translocation of masses. C. R. (Dokl.) Acad. Sci. URSS 37 (1942) 199–201. [Google Scholar]
  25. L.V. Kantorovič and G.Š. Rubinšteĭn, On a space of completely additive functions. Vestnik Leningrad. Univ. 13 (1958) 52–59. [MathSciNet] [Google Scholar]
  26. H. Kellerer, Duality theorems for marginal problems. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 67 (1984) 399–432. [CrossRef] [MathSciNet] [Google Scholar]
  27. C. Léonard, A saddle-point approach to the Monge–Kantorovich transport problem. ESAIM : COCV 17 (2011) 682–704. [CrossRef] [EDP Sciences] [Google Scholar]
  28. R. McCann, Existence and uniqueness of monotone measure-preserving maps. Duke Math. J. 80 (1995) 309–323. [CrossRef] [MathSciNet] [Google Scholar]
  29. T. Mikami, A simple proof of duality theorem for Monge–Kantorovich problem. Kodai Math. J. 29 (2006) 1–4. [CrossRef] [MathSciNet] [Google Scholar]
  30. T. Mikami and M. Thieullen, Duality theorem for the stochastic optimal control problem. Stoch. Proc. Appl. 116 (2006) 1815–1835. [CrossRef] [Google Scholar]
  31. D. Ramachandran and L. Rüschendorf, A general duality theorem for marginal problems. Probab. Theory Relat. Fields 101 (1995) 311–319. [CrossRef] [Google Scholar]
  32. D. Ramachandran and L. Rüschendorf, Duality and perfect probability spaces. Proc. Amer. Math. Soc. 124 (1996) 2223–2228. [CrossRef] [MathSciNet] [Google Scholar]
  33. M. Reed and B. Simon, Methods of Modern Mathematical Physics, I : Functional Analysis. Academic Press (1980). [Google Scholar]
  34. L. Rüschendorf, On c-optimal random variables. Stat. Probab. Lett. 27 (1996) 267–270. [CrossRef] [MathSciNet] [Google Scholar]
  35. K. Schmidt, A cylinder flow arising from irregularity of distribution. Compositio Math. 36 (1978) 225–232. [MathSciNet] [Google Scholar]
  36. W. Schachermayer and J. Teichman, Characterization of optimal transport plans for the Monge–Kantorovich problem. Proc. Amer. Math. Soc. 137 (2009) 519–529. [CrossRef] [MathSciNet] [Google Scholar]
  37. A. Szulga, On minimal metrics in the space of random variables. Teor. Veroyatnost. i Primenen. 27 (1982) 401–405. [MathSciNet] [Google Scholar]
  38. A.S. Üstünel, A necessary, and sufficient condition for invertibility of adapted perturbations of identity on Wiener space. C. R. Acad. Sci. Paris, Ser. I 346 (2008) 897–900. [CrossRef] [Google Scholar]
  39. A.S. Üstünel and M. Zakai, Sufficient conditions for the invertibility of adapted perturbations of identity on the Wiener space. Probab. Theory Relat. Fields 139 (2007) 207–234. [CrossRef] [Google Scholar]
  40. C. Villani, Topics in Optimal Transportation, in Graduate Studies in Mathematics. Amer. Math. Soc., Providence RI 58 (2003). [Google Scholar]
  41. C. Villani, Optimal Transport, Old and New, in Grundlehren der mathematischen Wissenschaften. Springer 338 (2009). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.