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Stochastic Analysis and Related Topics VII: Proceedings of the Seventh Silivri Workshop / Edition 1

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Overview

Stochastic 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
* stochastic 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 stochastic 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 stochastic 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

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Product Details

  • ISBN-13: 9780817642006
  • Publisher: Birkhauser Verlag
  • Publication date: 5/7/2009
  • Series: Progress in Probability Series , #48
  • Edition description: 2001
  • Edition number: 1
  • Pages: 252
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.63 (d)

Table of Contents

Preface
• 1. Heat Kernel Analysis on Lie Groups / L. Gross
• 2. Hausdorff—Gauss Measures / D. Feyel
• 3. Short Time Asymptotics of Certain Infinite Dimensional Diffusion Processes / S. Aida and H. Kawabi
• 4. Stokes' and Ito's Formulae for Anticipative Processes in Two Dimensions with Non-Monotonous Time Scale / S. Amine
• 5. The Complex Brownian Motion as a Weak Limit of Processes Constructed from a Poisson Process / X. Bardina
• 6. Large Deviation of Diffusion Processes with Discontinuous Drift / T.-S. Chiang and S.-J. Sheu
• 7. A Skohorod—Stratonovitch Integral for the Fractional Brownian Motion / L. Decreusefond
• 8. Density Estimate in Small Time for Jump Processes with Singular L\'evy Measures / Y. Ishikawa
• 9. Variational Calculus for a L\'evy process Based on a Lie Group / N. Privault
• 10. Sharp Laplace Asymptotics for a Hyperbolic SPDE / C. Rovira and S. Tindel
• 11. Damped Logarithmic Sobolev Inequality on the Wiener Space / A.S. Ustunel

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