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. Biane, P., Pitman, J., and Yor, M. (2001), Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions, Bull. A.M.S. (N.S.), 38, 435 - 465.
  2. Cameron, R.H. and Martin, W.T. (1944), The Wiener measure of Hilbert neighborhoods in the space of real continuous functions, Jour. Math. Phys. Massachusetts Inst. Technology, 23 195 - 209. Math. Review 6,132a
  3. Cameron, R.H. and Martin, W.T. (1945), Transformations of Wiener integrals under a general class of linear transformations, Trans. Amer. Math. Soc., 58, 184 - 219. Math. Review 7,127c
  4. Dunford, N. and Schwartz, J.T. (1963), Linear operators, Part II, Interscience, New York. Math. Review 32 #6181
  5. Donati-Martin, C. and Yor, M. (1991), Fubini's theorem for double Wiener integrals and the variance of the Brownian path, Ann. Inst. Henri Poincaré, 27, 181-200. Math. Review 92m:60072
  6. Hörmander, L. (1990), The Analysis of Linear Partial Differential Operators I, 2nd ed., Springer, Berlin. Math. Review 91m:35001b
  7. Ikeda, N. and Manabe, S. (1993), Asymptotic formulae for stochastic oscillatory integrals, in ``Asymptotic Problems in Probability Theory: Wiener Functionals and Asymptotics'' WHERE article_id=ed. by K.D.Elworthy and N.Ikeda, Longman, 136-155. Math. Review 97j:60098
  8. Ikeda, N. and Watanabe, S. (1989), Stochastic Differential Equations and Diffusion Processes, 2nd ed., North-Holland/Kodansha, Amsterdam/Tokyo. Math. Review 90m:60069
  9. Itô, K. and Nisio, M. (1968), On the convergence of sums of independent Banach space valued random variables Osaka Jour. Math., 5, 35 - 48. Math. Review 38 #3897
  10. Jorgenson, J. and Lang, S. (1993), Basic analysis of regularized series and products, Lect. Notes in Math. 1564, Springer, Berlin. Math. Review 95e:11094
  11. Kuo, H.-H. (1975), Gaussian measures in Banach spaces, Lect. Notes in Math. 463, Springer, Berlin. Math. Review 57 #1628
  12. Lévy, P. (1950), Wiener's random function, and other Laplacian random functions, in ``Proc. Second Berkeley Symp. Math. Stat. Prob. II'' WHERE article_id= U.C. Press, Berkeley, 171 - 186. Math. Review 13,476b
  13. Lyons, T. (1995), The interpretation and solution of ordinary differential equations driven by rough signals, Proc. Symposia in Pure Math. 57, 115 - 128. Math. Review 96d:34076
  14. Malliavin, P. (1985), Analyticité transverse d'opérateurs hypoelliptiques C3 sur des fibrés principaux, Spectre équivariant et courbure, C. R. Acad. Sc. Paris, 301, 767-770. Math. Review 87a:35051
  15. Pitman, J. and Yor, M. Infinitely divisible laws associated with hyperbolic functions, preprint.
  16. Sato, K. (1999), Lévy Processes and Infinitely Divisible Distributions, Cambridge Univ. Press, Cambridge.
  17. Sugita, H. and Taniguchi, S. (1998), Oscillatory integrals with quadratic phase function on a real abstract Wiener space, J. Funct. Anal. 155, 229-262. Math. Review 99e:60126
  18. Taniguchi, S. (1996), On Ricci curvatures of hypersurfaces in abstract Wiener spaces, J. Funct. Anal., 136, 226-244. Math. Review 97j:60101
  19. Whittaker, E.T. and Watson, G.N. (1927), A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, Cambridge, Math. Review 97k:01072
Bookmark and Share


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