Overview
- Editors:
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Evarist Giné
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Departments of Mathematics & Statistics, University of Connecticut, Storrs, USA
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David M. Mason
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Department of Food and Resource Econ., University of Delaware, Newark, USA
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Jon A. Wellner
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Department of Statistics, University of Washington, Seattle, USA
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Table of contents (32 papers)
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Inequalities
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- Victor H. de la Peña, Michael J. Klass, Tze Leung Lai
Pages 3-11
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- Evarist Giné, Rafał Latała, Joel Zinn
Pages 13-38
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- Friedrich Götze, Andrei Yu. Zaitsev
Pages 39-47
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General Empirical Process Theory
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- Peter Gaenssler, Daniel Rost
Pages 79-87
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- Dragan Radulović, Marten Wegkamp
Pages 89-105
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- Aad van der Vaart, Jon A. Wellner
Pages 115-133
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Gaussian Processes
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Front Matter
Pages 135-135
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Strong Approximation and Embedding
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Front Matter
Pages 181-181
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- Paul Deheuvels, Uwe Einmahl, David M. Mason
Pages 183-205
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About this book
High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. Parallel to this work on probability in Banach spaces, classical proba bility and empirical process theory were enriched by the development of powerful results in strong approximations.
Editors and Affiliations
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Departments of Mathematics & Statistics, University of Connecticut, Storrs, USA
Evarist Giné
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Department of Food and Resource Econ., University of Delaware, Newark, USA
David M. Mason
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Department of Statistics, University of Washington, Seattle, USA
Jon A. Wellner
