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Transport problems and optimal couplings

Description of the project:
The solving of transport problems and the determination of optimal couplings dates back to the question in Monge 1781 and then to papers of Kantorovich and Rubinstein in the fourties. Lately this problem was handled general form, and it has found great interest in many applications in analysis, limit theory, and algorithms. A two-volume treatise on transport theory appeared recently at Springer (Rachev/Rüschendorf). In these books a survey of duality theory of transport problems and their manifold applications is given. Intensive work is going on on the connection between perfectnes and the validity of duality therems (Ramachandran/Rüschendorf). It turns out that, in some way, the most general duality theorems can be expected only in the context of perfect measure spaces. Optimal transport-plans could be determined for various concrete problems.

Phone: 0761/203-5665
Email: ruschen@stochastik.uni-freiburg.de
Runtime:
Start of project: 1994
End of project: 2001
Project Management:
Albert-Ludwigs-University Freiburg
Prof. Dr. Ludger Rüschendorf
Abteilung für Mathematische Stochastik
Prof. Dr. Ludger Rüschendorf
Ernst-Zermelo-Straße 1
79104 Freiburg
Germany

Phone: 0761/203-5664
Fax: 0761/203-5661
Email: sekretariat@stochastik.uni-freiburg.de
http://www.stochastik.uni-freiburg.de/rueschendorf
Actual Research Report
Keywords:
    Monge-Kantorovich Transportproblem, Anwendung auf optimale C
project-related publications:
  • Rachev S.T., Rüschendorf L.: Mass Transportation Problems. Vol. I: Theory.Springer, 1998.
  • Rachev S.T., Rüschendorf L.: Mass Transportation Problems. Vol. II: Applications.Springer, 1998.
  • Uckelmann L.: Über das Monge-Kantorovich Transportproblem und dessen Verallgemeinerungen Dissertation Universität Freiburg, 1998.
  • Rüschendorf L, Uckelmann L: On optimal multivariate couplings. In: Benes V, Stepan I (Hrsg.): Proceedings of Prague 1996 conference on marginal problems. Kluwer, 1997; 261-274.
  • Uckelmann L.: Optimal couplings between onedimensional distributions. In: Benes V., Stepan I. (Hrsg.): Proceedings of Prague 1996 conference on marginal problems Kluwer, 1997; 275-281.
  • Cuesta J, Matran C, Rachev S.T, Rüschendorf L: Mass transportation problems in probability theory. Math. Scientist, 1996; 21: 34-72.
  • Ramachandran D, Rüschendorf L: Duality and perfect probability spaces. Trans. Amer. Math. Soc., 1996; 124: 2223-2228.
  • Ramachandran D, Rüschendorf L: A general duality theorem for marginal problems. Prob. Theory Rel. Fields, 1995; 101: 311-319.
  • Rüschendorf L: Optimal solutions of multivariate coupling problems. Applic. Mathematicae, 1995; 23: 325-338.