Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities

François Bolley; Cédric Villani

Annales de la Faculté des sciences de Toulouse : Mathématiques (2005)

  • Volume: 14, Issue: 3, page 331-352
  • ISSN: 0240-2963

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Bolley, François, and Villani, Cédric. "Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities." Annales de la Faculté des sciences de Toulouse : Mathématiques 14.3 (2005): 331-352. <http://eudml.org/doc/73650>.

@article{Bolley2005,
author = {Bolley, François, Villani, Cédric},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Csiszár-Kullback-Pinsker inequality; Wasserstein distance; Kullback information; transportation inequalities; random dynamical system},
language = {eng},
number = {3},
pages = {331-352},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities},
url = {http://eudml.org/doc/73650},
volume = {14},
year = {2005},
}

TY - JOUR
AU - Bolley, François
AU - Villani, Cédric
TI - Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2005
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 14
IS - 3
SP - 331
EP - 352
LA - eng
KW - Csiszár-Kullback-Pinsker inequality; Wasserstein distance; Kullback information; transportation inequalities; random dynamical system
UR - http://eudml.org/doc/73650
ER -

References

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  2. [2] Bobkov ( S. ), Gentil ( I.), Ledoux ( M.). - Hypercontractivity of Hamilton-Jacobi equations, J. Math. Pures Appl.80, 7, p. 669-696 (2001). Zbl1038.35020MR1846020
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  4. [4] Cattiaux ( P. ) , Guillin ( A.). - A criterion for Talagrand's quadratic transportation cost, Preprint (2003). Available at http://arxiv.org/abs/math.PR/0312081 
  5. [5] Djellout ( H.), Guillin ( A.), Wu ( L.). — Transportation cost-information inequalities for random dynamical systems and diffusions , Ann. Probab., 32, 3B, p. 2702-2732 (2004). Zbl1061.60011MR2078555
  6. [6] Ledoux ( M.). - The concentration of measure phenomenon, vol. 89 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI (2001). Zbl0995.60002MR1849347
  7. [7] Marton ( K.). - Bounding @DO&gt;d@FO&gt;-distance by information divergence: a method to prove measure concentration, Ann. Probab.24, p. 857-866 (1996). Zbl0865.60017MR1404531
  8. [8] Otto ( F.) , Villani ( C.). — Generalization of an inequality by Talagrand, and links with the logarithmic Sobolev inequality, J. Funct. Anal.173, p. 361-400 (2000). Zbl0985.58019MR1760620
  9. [9] Rachev ( S.T. ). — Probability metrics and the stability of stochastic models, John Wiley & Sons Ltd., Chichester (1991). Zbl0744.60004
  10. [10] Talagrand ( M.). - Transportation cost for Gaussian and other product measures, Geom. Funct. Anal.6, 3, p. 587-600 (1996). Zbl0859.46030MR1392331
  11. [11] Villani ( C.). — Topics in optimal transportation , vol. 58 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI (2003). Zbl1106.90001MR1964483

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