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High Dimensional Probability III

  • Jørgen Hoffmann-Jørgensen
  • Jon A. Wellner
  • Michael B. Marcus

Part of the Progress in Probability book series (PRPR, volume 55)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Measures on General Spaces and Inequalities

  3. Gaussian Processes

  4. Limit Theorems

  5. Local Times

    1. Front Matter
      Pages 175-175
    2. Raouf Ghomrasni, Goran Peskir
      Pages 177-192
    3. Michael B. Marcus
      Pages 193-202
  6. Large and Small Deviations

    1. Front Matter
      Pages 203-203
    2. Miguel A. Arcones
      Pages 205-223
    3. Xia Chen, Wenbo V. Li
      Pages 225-238
  7. Density Estimation

    1. Front Matter
      Pages 239-239
    2. Evarist Giné, Vladimir Koltchinskii, Lyudmila Sakhanenko
      Pages 241-253
  8. Statistics via Empirical Process Theory

    1. Front Matter
      Pages 293-293
    2. Peter Gaenssler, Daniel Rost
      Pages 313-320
    3. Dragan Radulović
      Pages 333-346

About these proceedings

Introduction

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.

Keywords

Deviations Estimator Limit theorems Measure theory Probability theory Random variable Stochastic processes mathematical statistics

Editors and affiliations

  • Jørgen Hoffmann-Jørgensen
    • 1
  • Jon A. Wellner
    • 2
  • Michael B. Marcus
    • 3
  1. 1.Department of Mathematical SciencesUniversity of AarhusArhus CDenmark
  2. 2.Department of StatisticsUniversity of WashingtonSeattleUSA
  3. 3.Department of MathematicsCity CollegeNew YorkUSA

Bibliographic information

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