Transportation cost inequalities on path and loop groups

Journal of Functional Analysis

Volumn 218, Issue 2, 2005, Pages 293-317

  Fang, Shizan ^a   Shao, Jinghai ^b  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Girsanov theorem; H distance; Heat measures; Loop groups; Wasserstein distance

Indexed keywords

EID: 11044233211     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2004.02.002     Document Type: Article

References (21)

1. Bobkov S. Gentil I. Ledoux M. Hypercontractivity of Hamilton-Jacobi equations J. Math. Pure Appl. 80 2001 669-696
2. H. Djellout, A. Guillin, L. Wu, Transportation cost-information inequalities for random dynamical systems and diffusions, Preprint, November 2002.
3. Driver B. The non-equivalence of Dirichlet form on path spaces Pitman Res. Notes Math. Ser. 310 1994 75-88
4. Driver B. Integration by parts and quasi-invariance for heat measures on loop groups J. Funct. Anal. 149 1997 470-547
5. Driver B. Lohrentz T. Logarithmic Sobolev inequalities for pinned loop groups J. Funct. Anal. 140 1996 381-448
6. Enchev O. Stroock D. Rademacher's theorem for Wiener functionals Ann. Probab. 23 1993 25-33
7. Fang S. Integration by parts formula and Logarithmic Sobolev inequality on the path space over loop groups Ann. Probab. 27 1999 664-683
8. Feyel D. Üstünel A. Measure transport on Wiener space and the Girsanov theorem C.R. Acad. Paris 334 2002 1025-1028
9. I. Gentil, Inégalités de Sobolev logarithmiques et hypercontractivité en mécanique statistique et en EDP, Thèse de Doctorat de l'Université Paul Sabatier, Toulouse, 2001.
10. Gross L. Logarithmic Sobolev inequalities on loop groups J. Funct. Anal. 102 1991 268-313
11. Gross L. Logarithmic Sobolev inequalities on Lie groups Illinois J. Math. 36 1992 447-490
12. Hino M. Ramirez J.A. Small-time Gaussian behavior of symmetric diffusion semigroups Ann. Probab. 31 2003 1254-1295
13. F. Hirsch, Measurable metrics and Gaussian concentration, Preprint 2003, Université d'Evry.
14. M. Ledoux, Concentration, transportation and functional inequalities, Instructional Conference on Combinatorial Aspects of Mathematical Analysis, Edinburgh, 25 March-5 April, 2002.
15. P. Malliavin, Hypoellipticity in infinite dimension, in: M. Pinsky (Ed.), Diffusion Processes and Related Problem in Analysis, Birkhaüser, Boston, pp. 17-33, 1989.
16. P. Malliavin, Naturality of quasi-invariance of some measure, in: A.B. Cruzeiro (Ed.), Proceedings of Lisbon Conference, Birkhaüser, Boston, Prog. Probab. 26 (1991) 144-154.
17. Malliavin P. Stochastic Analysis 1997 Springer New York
18. Otto F. Villani C. Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality J. Funct. Anal. 173 2000 361-400
19. Revuz D. Yor M. Continuous Martingales and Brownian Motion 1991 Springer New York
20. Talagrand M. Transportation cost for Gaussian and other product measures Geom. Funct. Anal. 6 1996 587-600
21. Wang F.Y. Probability distance inequalities on Riemannian manifolds and path spaces J. Funct. Anal. 206 2004 167-190