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Stochastic Inequalities and Applications

  • Conference proceedings
  • © 2003

Overview

Editors:
  1. Evariste Giné

    1. Department of Mathematics, U-3009, University of Connecticut, Storrs, USA

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  2. Christian Houdré

    1. Laboratoire d’Analyse et de Mathématiques Appliquées CNRS UMR 8050, Université de Paris XII, Créteil Cedex, France
      Georgia Institute of Technology, School of Mathematics, Atlanta, USA

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  3. David Nualart

    1. Facultat de Matemàtiques, Universitat de Barcelona, Barcelona, Spain

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  • Articles are representative of the state of the art in stochastic inequalities
  • Broad scope, many applications are discussed

Part of the book series: Progress in Probability (PRPR, volume 56)

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Table of contents (20 papers)

  1. Front Matter

    Pages i-viii
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  2. Geometric Inequalities

    1. Front Matter

      Pages 1-1
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    2. Large Deviations of Typical Linear Functionals on a Convex Body with Unconditional Basis

      • Sergey G. Bobkov, Fedor L. Nazarov
      Pages 3-13

    3. A Concentration Inequality on Riemannian Path Space

      • Christian Houdré, Nicolas Privault
      Pages 15-21

    4. A Remark on Unified Error Exponents: Hypothesis Testing, Data Compression and Measure Concentration

      • Ioannis Kontoyiannis, Ali Devin Sezer
      Pages 23-32

    5. Concentration Inequalities for Convex Functions on Product Spaces

      • Paul-Marie Samson
      Pages 33-52

  3. Independent Random Vectors, Chaos, Martingales and Lévy Processes

    1. Front Matter

      Pages 53-53
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    2. Exponential Inequalities, with Constants, for U-statistics of Order Two

      • Christian Houdré, Patricia Reynaud-Bouret
      Pages 55-69

    3. On a.s. Unconditional Convergence of Random Series in Banach Spaces

      • Stanisław Kwapień, Vaja Tarieladze
      Pages 71-75

    4. Moment and Tail Estimates for Multidimensional Chaos Generated by Positive Random Variables with Logarithmically Concave Tails

      • Rafał Latała, Rafał Łochowski
      Pages 77-92

    5. A Quantitative Law of Large Numbers via Exponential Martingales

      • Malwina J. Luczak
      Pages 93-111

    6. Sufficient Conditions for Boundedness of Moving Average Processes

      • Michael B. Marcus, Jan Rosiński
      Pages 113-128

    7. Notes on the Speed of Entropic Convergence in the Central Limit Theorem

      • Laurent Miclo
      Pages 129-156

    8. On a Nonsymmetric Version of the Khinchine-Kahane Inequality

      • Krzysztof Oleszkiewicz
      Pages 157-168

    9. Dimensionality Reduction in Extremal Problems for Moments of Linear Combinations of Vectors with Random Coefficients

      • Iosif Pinelis
      Pages 169-185

  4. Empirical Processes

    1. Front Matter

      Pages 187-187
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    2. Moderate Deviations of Empirical Processes

      • Miguel A. Arcones
      Pages 189-212

    3. Concentration Inequalities for Sub-Additive Functions Using the Entropy Method

      • Olivier Bousquet
      Pages 213-247

    4. Ratio Limit Theorems for Empirical Processes

      • Evarist Giné, Vladimir Koltchinskii, Jon A. Wellner
      Pages 249-278

    5. Asymptotic Distributions of Trimmed Wasserstein Distances Between the True and the Empirical Distribution Function

      • Erich Haeusler, David M. Mason
      Pages 279-298
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Keywords

About this book

Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to many applications particularly in stochastic analysis. The broad range and the high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers in the above areas.

Editors and Affiliations

  • Department of Mathematics, U-3009, University of Connecticut, Storrs, USA

    Evariste Giné

  • Laboratoire d’Analyse et de Mathématiques Appliquées CNRS UMR 8050, Université de Paris XII, Créteil Cedex, France

    Christian Houdré

  • Georgia Institute of Technology, School of Mathematics, Atlanta, USA

    Christian Houdré

  • Facultat de Matemàtiques, Universitat de Barcelona, Barcelona, Spain

    David Nualart

Bibliographic Information

  • Book Title: Stochastic Inequalities and Applications

  • Editors: Evariste Giné, Christian Houdré, David Nualart

  • Series Title: Progress in Probability

  • DOI: https://doi.org/10.1007/978-3-0348-8069-5

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2003

  • Hardcover ISBN: 978-3-7643-2197-0Published: 24 October 2003

  • Softcover ISBN: 978-3-0348-9428-9Published: 23 October 2012

  • eBook ISBN: 978-3-0348-8069-5Published: 06 December 2012

  • Series ISSN: 1050-6977

  • Series E-ISSN: 2297-0428

  • Edition Number: 1

  • Number of Pages: VIII, 367

  • Topics: Probability Theory and Stochastic Processes

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