Stochastic Analysis and Related Topics VII: Proceedings of the Seventh Silivri Workshop (Progress in Probability, 48)

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.

Shastic analysis has proved to be one of the most widely applicable mathematical tools available to researchers in a variety of scientific and engineering disciplines. One of the most challenging subjects in relation to physics concerns an analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of the path and loop space on a Lie group. In this volume an up-to-date survey of this topic is given by L. Gross. Another concise but complete survey of the Hausdorff measure on Wiener space and its applications to Malliavin Calculus is given by D. Feyel.
Other survey articles deal with a variety of rich topics:

* short time asymptotics of diffusion processes with values in infinite dimensional manifolds
* large deviations of diffusions with discontinuous drifts
* shastic integration with respect to the fractional Brownian motion (which is not a semimartingale)
* Stokes' formula for the Brownian sheet
* a new family of logarithmic Sobolev inequalities via the Girsanov Theorem

The broad coverage of various subjects demonstrates the powerful shastic techniques of prominent researchers. This volume is an outgrowth of the Seventh Silivri Workshop. It will serve as a good reference text for graduate students and those working in shastic analysis, as well as mathematical economists treating modeling systems with long memory.
Contributors: S. Aida, S. Amine, X. Bardina, T.-S. Chiang, L. Decreusefond, D. Feyel, L. Gross, Y. Ishikawa, H. Kawabi, N. Privault, C. Rovira, S.-J. Sheu, S. Tindel, A.S. Ustunel

Front Matter....Pages i-vii Heat Kernel Analysis on Lie Groups....Pages 1-58 Hausdorff-Gauss Measures....Pages 59-76 Short Time Asymptotics of a Certain Infinite Dimensional Diffusion Process....Pages 77-124 Stokes and Itô’s Formulae for Anticipative Processes in Two Dimensions with Non-Monotonous Time....Pages 125-147 The Complex Brownian Motion as a Weak Limit of Processes Constructed from a Poisson Process....Pages 149-158 Large Deviation of Diffusion Processes with Discontinuous Drift....Pages 159-175 A Skohorod-Stratonovitch Integral for the Fractional Brownian Motion....Pages 177-198 Density Estimate in Small Time for Jump Processes with Singular Lévy Measures....Pages 199-206 Variational Calculus for a Lévy Process Based on a Lie Group....Pages 207-223 Sharp Laplace Asymptotics for a Hyperbolic SPDE....Pages 225-244 Damped Logarithmic Sobolev Inequality on the Wiener Space....Pages 245-249 Back Matter....Pages 251-252