Caractérisation d'une solution optimale au problème de Monge-Kantorovitch

Taoufiq Abdellaoui; Henri Heinich

Bulletin de la Société Mathématique de France (1999)

  • Volume: 127, Issue: 3, page 429-443
  • ISSN: 0037-9484

How to cite

top

Abdellaoui, Taoufiq, and Heinich, Henri. "Caractérisation d'une solution optimale au problème de Monge-Kantorovitch." Bulletin de la Société Mathématique de France 127.3 (1999): 429-443. <http://eudml.org/doc/87813>.

@article{Abdellaoui1999,
author = {Abdellaoui, Taoufiq, Heinich, Henri},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Monge-Kantorovich problem; probabilities with fixed marginals; cyclic monotonicity; subdifferential},
language = {fre},
number = {3},
pages = {429-443},
publisher = {Société mathématique de France},
title = {Caractérisation d'une solution optimale au problème de Monge-Kantorovitch},
url = {http://eudml.org/doc/87813},
volume = {127},
year = {1999},
}

TY - JOUR
AU - Abdellaoui, Taoufiq
AU - Heinich, Henri
TI - Caractérisation d'une solution optimale au problème de Monge-Kantorovitch
JO - Bulletin de la Société Mathématique de France
PY - 1999
PB - Société mathématique de France
VL - 127
IS - 3
SP - 429
EP - 443
LA - fre
KW - Monge-Kantorovich problem; probabilities with fixed marginals; cyclic monotonicity; subdifferential
UR - http://eudml.org/doc/87813
ER -

References

top
  1. [1] ABDELLAOUI (T.), HEINICH (H.). — Sur la distance de deux lois de probabilités dans le cas vectoriel, C. R. Acad. Sci. Paris, t. 319, série I, 1994, p. 981-984. Zbl0808.60008MR95h:60007
  2. [2] BICKEL (P.J.), FREEDMAN (D.A.). — Some asymptotic Theory for the Bootstrap, Ann. Statis., t. 9, 1981, p. 1196-1217. Zbl0449.62034MR83a:62051
  3. [3] BELILI (N.), HEINICH (H.). — Mass Transport Problem and Derivation, à paraître dans Appli. Mathematicae, 1999. Zbl0998.60012MR2001a:60016
  4. [4] CUESTA-ALBERTOS (J.A.), MATRÁN (C.). — Notes on the Wasserstein Metric in Hilbert Spaces, Ann. Prob., t. 17, 1989, p. 1264-1276. Zbl0688.60011MR90k:60029
  5. [5] CUESTA-ALBERTOS (J.A.), TUERO-DIAZ (A.). — A Characterization for the Solution of the Monge-Kantorovich Mass Transference Problem, Statist. Probab. Lett., t. 16, 1993, p. 147-152. Zbl0765.60010MR94g:60024
  6. [6] CUESTA-ALBERTOS (J.A.), MATRÁN (C.), RACHEV (S.T.), RÜSCHENDORF (L.). — Mass Transportation Problems in Probability Theory, App. Prob. Trust., t. 21, 1996, p. 1-39. MR97c:60045
  7. [7] COHN (D.L.). — Measure Theory. — Birkhäuser, 1980. Zbl0436.28001MR81k:28001
  8. [8] EKELAND (I.), TEMAM (R.). — Analyse convexe et problèmes variationnels. — Dunod, 1974. Zbl0281.49001MR57 #3931a
  9. [9] GANGBO (W.), MCCANN (R.J.). — Optimal Maps in Monge's Mass Transport Problem, C. R. Acad. Sci. Paris, t. 321, Série I, 1995, p. 1653-1658. Zbl0858.49002MR96i:49004
  10. [10] GANGBO (W.), MCCANN (R.J.). — The Geometry of optimal Transportation, Acta Math., t. 177, 1996, p. 113-161. Zbl0887.49017MR98e:49102
  11. [11] KNOTT (M.), SMITH (C.S.). — Note on the optimal Transportation of Distributions, J. Opt. Theor. Appl., t. 52, 1987, p. 323-329. Zbl0586.49005MR88d:90076
  12. [12] KELLERER (H.). — Duality Theorems for Marginal Problems, Z. Wahrsh. Verw. Gebiete, t. 67, 1984, p. 399-432. Zbl0535.60002MR86i:28010
  13. [13] MCCANN (R.J.). — Existence and Uniqueness of monotone measure-preserving Maps, Duke. Math. J., t. 80, 1995, p. 309-323. Zbl0873.28009MR97d:49045
  14. [14] RACHEV (S.T.), RÜSCHENDORF (L.). — A Characterization of random Variables with minimum L2 Distance, J. Multivariate Anal., t. 32, 1990, p. 48-54. Zbl0688.62034
  15. [15] RACHEV (S.T.). — Probability Metrics and the Stability of stochastic Models. — Wiley, New York, 1991. Zbl0744.60004MR93b:60012
  16. [16] ROCKAFELLAR (R.T.). — Convex Analysis. — Princeton University Press, 1972. 
  17. [17] RÜSCHENDORF (L.). — Optimal Solutions of multivariate coupling Problems, Appl. Mathematicae, t. 23, 1995, p. 325-338. Zbl0844.62047MR96k:60043
  18. [18] ZAJIČEK (L.). — On the Differentiation of convex Functions in finite and infinite dimensional Spaces, Czechoslovak Math. J., t. 29, 1979, p. 340-348. Zbl0429.46007MR80h:46063

NotesEmbed ?

top

You must be logged in to post comments.