Concentration Inequalities for Sums and Martingales

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.

List of contents

Classical Results.- Concentration Inequalities for Sums.- Concentration Inequalities for Martingales.- Applications in Probability and Statistics.

Summary

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.

Product details

• Authors: Bernar Bercu, Bernard Bercu, Bernar Delyon, Bernard Delyon, Emmanuel Rio
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2015
• EAN: 9783319220987
• ISBN: 978-3-31-922098-7
• No. of pages: 120
• Dimensions: 160 mm x 233 mm x 6 mm
• Weight: 240 g
• Illustrations: X, 120 p. 9 illus. in color.
• Series: SpringerBriefs in Mathematics; SpringerBriefs in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; C, History, Mathematics, Mathematics and Statistics, Probability Theory and Stochastic Processes, Complex analysis, complex variables, Probabilities, Stochastics, Probability Theory, History of mathematics, History of Mathematical Sciences, Functions of complex variables, Several Complex Variables and Analytic Spaces