High Dimensional Probability III: 55 (Progress in Probability, 55) - Hardcover

Hardcover

ISBN 10: 3764321873 ISBN 13: 9783764321871

Publisher: Birkhäuser, 2003

Synopsis

The title High Dimensional Probability is an attempt to describe the many trib­ utaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970's. In each of these fields it is necessary to consider large classes of stochastic processes under minimal conditions. There are rewards in re­ search of this sort. One can often gain deep insights, even about familiar processes, by stripping away details that in hindsight turn out to be extraneous. Many of the problems that motivated researchers in the 1970's were solved. But the powerful new tools created for their solution, such as randomization, isoperimetry, concentration of measure, moment and exponential inequalities, chaining, series representations and decoupling turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new ap­ proach to the study of aspects of Levy processes and Markov processes in general. Papers on these topics as well as on the continuing study of Gaussian processes and probability in Banach are included in this volume.

About this title

Synopsis

The title High Dimensional Probability is used to describe the many tributaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970s. Many of the problems that motivated researchers at that time were solved. But the powerful new tools created for their solution, such as randomization, isoperimetry, concentration of measure, moment and exponential inequalities, chaining, series representations, and decoupling turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new approach to the study of aspects of Levy processes and Markov processes in general.The papers in this book reflect these broad categories. They are divided into seven sections: - measures on general spaces and inequalities- Gaussian processes- limit theorems- local times- large and small deviations- density estimation- statistics via empirical process theory.

Edition details

• Publisher: Birkhäuser
• Publication date: 2003
• Language: English
• ISBN 10: 3764321873
• ISBN 13: 9783764321871
• Binding: Hardcover
• Number of pages: 354
• Editor: Hoffmann-Joergensen Joergen, Marcus Michael B., Wellner Jon A.