The Sard Inequality on Two Non-Gaussian Spaces

  • Nicolas Privault
Conference paper
Part of the Progress in Probability book series (PRPR, volume 42)

Abstract

We prove the Sard inequality in infinite dimensions for the exponential and uniform densities and obtain an extension of the corresponding change of variables formula.

Keywords

Univer 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    C. Castaing and M. Valadier. Convex analysis and measurable multifunctions, volume 580 of Lecture Notes in Mathematics. Springer Verlag, Berlin/New York, 1977.Google Scholar
  2. [2]
    N. Dunford and J. T. Schwartz. Linear Operators, volume II. Interscience publishers, New York, 1957.Google Scholar
  3. [3]
    H. Federer. Geometric Measure Theory. Springer-Verlag, Berlin/New York, 1969.MATHGoogle Scholar
  4. [4]
    E. Getzler. Degree theory for Wiener maps. Journal of Functional Analysis, 68:388–403, 1986.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    S. Kusuoka. The nonlinear transformation of Wiener measure on Banach space and its absolute continuity. Journal of the Faculty of Science of Tokyo University, Section IA, Mathematics, 29:567–598, 1982.MathSciNetMATHGoogle Scholar
  6. [6]
    D. Nualart. Markov fields and transformations of the Wiener measure. In Tom Lindstrøm, Bernt Øksendal, and A. Süleyman Üstünel, editors, The Proceedings of the Fourth Oslo-Silivri Workshop on Stochastic Analysis, volume 8 of Stochastics Monographs. Gordon and Breach, 1993.Google Scholar
  7. [7]
    D. Nualart. The Malliavin Calculus and Related Topics. Probability and its Applications. Springer-Verlag, Berlin/New York, 1995.Google Scholar
  8. [8]
    N. Privault. Absolute continuity in infinite dimension and anticipating stochastic calculus. To appear in Potential Analysis.Google Scholar
  9. [9]
    N. Privault. Calcul des variations stochastique pour la mesure de densité uniforme. Potential Analysis, 7(2):577–601, 1997MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    N. Privault. Girsanov theorem for anticipative shifts on Poisson space. Probability Theory and Related Fields, 104:61–76, 1996.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    R. Ramer. On nonlinear transformations of Gaussian measures. Journal of Functional Analysis, 15:166–187, 1974.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    J.T. Schwartz. Nonlinear Functional Analysis. Gordon and Breach, New York, 1969.MATHGoogle Scholar
  13. [13]
    A.S. Üstünel. An Introduction to Analysis on Wiener Space, volume 1610 of Lecture Notes in Mathematics. Springer Verlag, Berlin/New York, 1995.Google Scholar
  14. [14]
    A.S. Üstünel and M. Zakai. Transformation of the Wiener measure under non-invertible shifts. Probability Theory and Related Fields, 99:485–500, 1994.MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    A.S. Üstünel and M. Zakai. Degree theory on Wiener space. Probability Theory and Related Fields, 108(2):259–280, 1997.MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    A.S. Üstünel and M. Zakai. The Sard inequality on Wiener space. Journal of Functional Analysis, 149:226–244, 1997.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Nicolas Privault

There are no affiliations available

Personalised recommendations