Overview
- Covers an extensive amount of different concentration inequalities for both sums and martingales
- Touches upon applications for probability and statistics
- Includes both classic and recent results on concentration inequalities
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (4 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Concentration Inequalities for Sums and Martingales
Authors: Bernard Bercu, Bernard Delyon, Emmanuel Rio
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-22099-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Authors 2015
Softcover ISBN: 978-3-319-22098-7Published: 12 October 2015
eBook ISBN: 978-3-319-22099-4Published: 29 September 2015
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: X, 120
Number of Illustrations: 9 illustrations in colour
Topics: Probability Theory and Stochastic Processes, History of Mathematical Sciences, Several Complex Variables and Analytic Spaces