Ebook: Stochastic Analysis and Related Topics VII: Proceedings of the Seventh Silivri Workshop

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.

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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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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
Content:
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 It?’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 L?vy Measures....Pages 199-206
Variational Calculus for a L?vy 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

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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
Content:
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 It?’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 L?vy Measures....Pages 199-206
Variational Calculus for a L?vy 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
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