Concentration Inequalities for Sums and Martingales

  • Bernard Bercu
  • Bernard Delyon
  • Emmanuel Rio
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Bernard Bercu, Bernard Delyon, Emmanuel Rio
    Pages 1-10
  3. Bernard Bercu, Bernard Delyon, Emmanuel Rio
    Pages 11-60
  4. Bernard Bercu, Bernard Delyon, Emmanuel Rio
    Pages 61-98
  5. Bernard Bercu, Bernard Delyon, Emmanuel Rio
    Pages 99-120

About this book

Introduction

The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales.

The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration inequalities for sums and martingales.

The second chapter deals with classical concentration inequalities for sums of independent random variables such as the famous Hoeffding, Bennett, Bernstein and Talagrand inequalities. Further results and improvements are also provided such as the missing factors in those inequalities.

The third chapter concerns concentration inequalities for martingales such as Azuma-Hoeffding, Freedman and De la Pena inequalities. Several extensions are also provided.

The fourth chapter is devoted to applications of concentration inequalities in probability and statistics.

Keywords

Bernstein's Inequalities Concentration Inequalities Gaussian Martingales Independent Random Variables Martingales

Authors and affiliations

  • Bernard Bercu
    • 1
  • Bernard Delyon
    • 2
  • Emmanuel Rio
    • 3
  1. 1.Institut de Mathématiques de Bordeaux, Université de BordeauxTalenceFrance
  2. 2.Institut de Recherche Math´ematique de Rennes, Universit´e de RennesRennesFrance
  3. 3.Laboratoire de Math´ematiques de Versailles, Universit´e de Versailles, St. Quentin en YvelinesVersaillesFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-22099-4
  • Copyright Information The Authors 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-22098-7
  • Online ISBN 978-3-319-22099-4
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book