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High Dimensional Probability

  • Conference proceedings
  • © 1998

Overview

Editors:
  1. Ernst Eberlein

    1. Institut für Mathematische Stochastik, Universität Freiburg, Freiburg, Germany

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  2. Marjorie Hahn

    1. Department of Mathematics, Tufts University, Medford, USA

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  3. Michel Talagrand

    1. Equipe d’analyse, Tour 46, Université Paris VI, Paris Cedex 05, France

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Part of the book series: Progress in Probability (PRPR, volume 43)

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Table of contents (20 papers)

  1. The Bootstrap of Empirical Processes for α-Mixing Sequences

    • Dragan Radulović
    Pages 315-330

  2. Back Matter

    Pages 332-335
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Keywords

About this book

What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings.

Editors and Affiliations

  • Institut für Mathematische Stochastik, Universität Freiburg, Freiburg, Germany

    Ernst Eberlein

  • Department of Mathematics, Tufts University, Medford, USA

    Marjorie Hahn

  • Equipe d’analyse, Tour 46, Université Paris VI, Paris Cedex 05, France

    Michel Talagrand

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