Stochastic Analysis and Related Topics VII

1. Front Matter

   Pages i-vii

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2. Heat Kernel Analysis on Lie Groups

   • L. Gross

   Pages 1-58

3. Hausdorff-Gauss Measures

   • D. Feyel

   Pages 59-76

4. Short Time Asymptotics of a Certain Infinite Dimensional Diffusion Process

   • Shigeki Aida, Hiroshi Kawabi

   Pages 77-124

5. Stokes and Itô’s Formulae for Anticipative Processes in Two Dimensions with Non-Monotonous Time

   • S. Amine

   Pages 125-147

6. The Complex Brownian Motion as a Weak Limit of Processes Constructed from a Poisson Process

   • X. Bardina

   Pages 149-158

7. Large Deviation of Diffusion Processes with Discontinuous Drift

   • T. S. Chiang, S. J. Sheu

   Pages 159-175

8. A Skohorod-Stratonovitch Integral for the Fractional Brownian Motion

   • L. Decreusefond

   Pages 177-198

9. Density Estimate in Small Time for Jump Processes with Singular Lévy Measures

   • Y. Ishikawa

   Pages 199-206

10. Variational Calculus for a Lévy Process Based on a Lie Group

    • N. Privault

    Pages 207-223

11. Sharp Laplace Asymptotics for a Hyperbolic SPDE

    • C. Rovira, S. Tindel

    Pages 225-244

12. Damped Logarithmic Sobolev Inequality on the Wiener Space

    • A. S. Üstünel

    Pages 245-249

13. Back Matter

    Pages 251-252

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One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro­ cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas­ tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log­ Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the­ art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.

• Brownian motion
• Girsanov theorem
• Martingale
• Measure
• Poisson process
• Semimartingale
• diffusion process
• fractional Brownian motion
• jump process

• Département Réseaux, Ecole Nationale Supérieure des Télécommunications, Paris Cedex 13, France

  Laurent Decreusefond, Ali Süleyman Üstünel

• Department of Mathematics, University of Oslo, Oslo, Norway

  Bernt K. Øksendal

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