The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. S. Aida, K. D. Elworthy, Differential calculus on path and loop spaces I. Logarithmic Sobolev inequalities on path spaces. C.R.A.S. Paris 321, (1995), 97-102 Math. Reviews number 96d:60078
  2. J.-M. Bismut, Large Deviations and the Malliavin Calculus. Birkhäuser (1984) Math. Reviews number 86f:58150
  3. M. Capitaine, E. P. Hsu, M. Ledoux, Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces. Elect. Comm. in Prob. 2, (1997), 71-81 Math. Reviews number 99b:60136
  4. A. B. Cruzeiro, P. Malliavin, Renormalized differential geometry on path space: structural equation, curvature. J. Funct. Anal. 140, (1996), 381-448. Math. Reviews number 97h:58175
  5. J. Deny, MÈthodes hilbertiennes en thÈorie du potentiel. CIME. Potential theory (1970) Math. Reviews number 44,1833
  6. J. Deny, J.-L. Lions, Espaces du type de Beppo-Levi. Ann. I. Fourier, III, (1953), 305-370. Math. Reviews number 17,646a
  7. B. K. Driver, A Cameron-Martin type quasi-invariance theorem for Brownian motion compact Riemannian manifold. J. Funct. Anal. 110, (1992), 272-376. Math. Reviews number 94a:58214
  8. B. K. Driver, The non-equivalence of the Dirichlet form on path spaces. Proc. U.S.-Japan bilateral seminar (1994) Math. Reviews number 97j:58158
  9. B. K. Driver, Integration by parts for heat kernel measure revisited. J. Math. Pures Appl. 76:9, 703-737 (1997) Math. Reviews number 98h:58198
  10. B. K. Driver, M. Röckner, Construction of diffusions on path and loop spaces of compact Riemannian manifolds. C.R.A.S. Paris, 315, (1992) 603-608 Math. Reviews number 93f:58246
  11. K. D. Elworthy, X. M. Li, A class of integration by parts formulae in stochastic analysis I. In Itô Stochastic Calculus and probability theory, 15-30. N. Ikeda and al., Springer Verlag, Tokyo (1996). Math. Reviews number 99e:60131
  12. K. D. Elworthy, Y. Le Jan, X. M. Li, Integration by parts formula for degenerate diffusion measures on path spaces. C.R.A.S. Paris, 323, (1996), 921-926 Math. Reviews number 97f:60127
  13. O. Enchev, D. Stroock, Towards a Riemannian geometry on the path space over a Riemannian manifold. J. Funct. Anal. 134, (1995) 392-416 Math. Reviews number 96m:58270
  14. S. Fang, InÈgalitÈ du type de PoincarÈ sur l'espace des chemins riemanniens. C.R.A.S. Paris, 318, (1994), 257-260 Math. Reviews number 94m:58238
  15. S. Fang, P. Malliavin, Stochastic Analysis on the Path Space of a Riemannian manifold. J. Funct. Anal. 118, (1993), 249-274 Math. Reviews number 94i:58209
  16. D. Feyel, Transformations de Hilbert-Riesz. CRAS, Paris, 310, (1990), 653-655 Math. Reviews number 91j:60114
  17. D. Feyel, A. de La Pradelle, ReprÈsentation d'espaces de Riesz-Banach sur des espaces quasi-topologiques. Bull. Acad. Royale de Belgique, 5eme sÈrie, t. LXIV, (1978-79), 340-350 Math. Reviews number 81h:31020
  18. D. Feyel, A. de La Pradelle, Espaces de Sobolev gaussiens. Ann. I. Fourier, 39:4 (1989) 875-908 Math. Reviews number 91e:60183
  19. D. Feyel, A. de La Pradelle, CapacitÈs gaussiennes. Ann. I. Fourier, 41:1 (1991) 49-76 Math. Reviews number 93b:60174
  20. D. Feyel, A. de La Pradelle, Brownian Processes in Infinite Dimension. Potential Analysis, 4, (1995), p.173-183 Math. Reviews number 96i:60044
  21. D. Feyel, A. de La Pradelle, On the approximate solutions of the Stratonovitch equation. Elect. J. Prob., 3:7, (1998), 1-14 Math. Reviews number 99j:60075
  22. D. Feyel, A. de La Pradelle, Fractional integrals and Brownian processes. Potential Analysis, 10, (1999), p.273-288 Math. Reviews number not available
  23. L. Gross, Logarithmic Sobolev inequalities. Amer. J. Math. 97, (1975) 1061-1083 Math. Reviews number 54 #8263
  24. L. Gross, Logarithmic Sobolev inequalities for the heat kernel of a Lie group. In White Noise Analysis (T. Hida and al., Eds), p. 108-130, World Scientific, Singapore-Teaneck-New Jersey (1990) Math. Reviews number 93f:58249
  25. E. P. Hsu, InÈgalitÈs de Sobolev logarithmiques sur un espace de chemins. C.R.A.S. Paris, 320, (1995) 1009-1012 Math. Reviews number 96e:58167
  26. N. Ikeda, S. Watanabe, Stochastic Differential Equation and Diffusion Processes. North-Holland, Amsterdam-Oxford-New York, (1981) Math. Reviews number 90m:60069
  27. P. Malliavin, Stochastic Analysis. Springer Verlag (1997) Math. Reviews number 99b:60073
  28. D. Nualart, The Malliavin calculus and Related Topics. Springer Verlag (1995) Math. Reviews number 96k:60130
  29. I. Shigekawa, A quasihomeomorphism of the Wiener space. Proc. Sump. Pure and Appllied Mathematics 57 (Cranston and Pinsky Ed.) Cornell, (1993) Am. Math. Soc. 8, (1995), 473-487 Math. Reviews number 96k:60134
  30. F. Y. Wang, Logarithmic Sobolev inequalities for diffusion processes with application to path space. Chinese J. Appl. Probab. Stat. 12:3, (1996) 255-264 Math. Reviews number not available
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.