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Concentration Inequalities for Sums and Martingales

Concentration Inequalities for Sums and Martingales by Bernard Bercu
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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.

Springer International Publishing; September 2015
131 pages; ISBN 9783319220994
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Title: Concentration Inequalities for Sums and Martingales
Author: Bernard Bercu; Bernard Delyon; Emmanuel Rio
 
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