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Talagrand’s T 2-transportation Inequality w.r.t. a Uniform Metric for Diffusions

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Abstract

Using the method of Girsanov transformation, we establish the Talagrand’s T 2-inequality for diffusion on the path space C([0,N],ℝd) with respect to a uniform metric, with the constant independent of N. This improves the known results for the L 2-metric.

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References

  1. Bobkov, S., Gentil, I., Ledoux, M. Hypercontractivity of Hamilton-Jacobi equations. J. Math. Pure Appl., 80: 669–696 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bobkov, S., Götze, F. Exponential integrability and transportation cost related to logarithmic Sobolev inequalities. J. Funct. Anal., 163: 1–28 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Djellout, H., Guillin, A., Wu, L. Transportation cost-information inequalities and applications to random dynamical systems and diffusions. Ann. Probab., 2004 (to appear)

  4. Fang, S., Shao, J. Transportation cost inequalities on path and loop groups. J. Funct. Anal., (to appear)

  5. Feyel, D., Ustunel, A.S. Measure transport on Wiener space and Girsanov theorem. CRAS Serie I, 334: 1025–1028 (2002)

    MATH  MathSciNet  Google Scholar 

  6. Feyel, D., Ustunel, A.S. The Monge-Kantorovitch problem and Monge-Amp`ere equation on Wiener space. Probab. Theor. Rel. Fields, 128(3): 347–385 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ledoux, M. The concentration of measure phenomenon Vol.89, Mathematical Surveys and Monographs, AMS, 2001

  8. Marton, K. Bounding d-distance by information divergence: a method to prove measure concentration. Ann. Probab., 24: 857–866 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  9. Marton, K. A measure concentration inequality for contracting Markov chains. Geom. Funct. Anal., 6: 556–571 (1997)

    Article  MathSciNet  Google Scholar 

  10. Otto, F., Villani, C. Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal., 173: 361–400 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Talagrand, M. Transportation cost for Gaussian and other product measures. Geom. Funct. Anal., 6: 587–600 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Villani, C. Topics in optimal transportation. Grad. Stud. Math. (58), American Mathematical Society, 2003

  13. Wang, F.Y. Probability distance inequalities on Rimaniann manifolds and path spaces. J. Funct. Anal., 206: 167–190 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Wang, F.Y. Transportation cost inequalities on path spaces over Riemannian manifolds. Illinois J. Math., 46: 1197–1206 (2002)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées, CNRS-UMR 6620, Université Blaise Pascal, 63177, Aubière, France

    Li-ming Wu

  2. Department Mathematics, Wuhan University, 430072, Wuhan, China

    Li-ming Wu

  3. Department Mathematics, Wuhan University, 430072, Wuhan, China

    Zheng-liang Zhang

Authors
  1. Li-ming Wu
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  2. Zheng-liang Zhang
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Correspondence to Li-ming Wu.

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Supported by the Yangtze professorship programm.

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Wu, Lm., Zhang, Zl. Talagrand’s T 2-transportation Inequality w.r.t. a Uniform Metric for Diffusions. Acta Mathematicae Applicatae Sinica, English Series 20, 357–364 (2004). https://doi.org/10.1007/s10255-004-0175-x

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  • DOI: https://doi.org/10.1007/s10255-004-0175-x

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