EAN: 9783319220987

SPRINGERBRIEFS IN MATHEMATICS CONCENTRATION I...

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.

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