Concentration Inequalities for Sums and Martingales
Concentration Inequalities for Sums and Martingales
Springer | Mathematics | October 31, 2015 | ISBN-10: 3319220985 | 120 pages | pdf | 1.76 mb
Springer | Mathematics | October 31, 2015 | ISBN-10: 3319220985 | 120 pages | pdf | 1.76 mb
by Bernard Bercu (Author), Bernard Delyon (Author), Emmanuel Rio (Author)
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
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.
Number of Illustrations and Tables
9 in colour
Topics
Probability Theory and Stochastic Processes
History of Mathematics
Several Complex Variables and Analytic Spaces
More info and Hardcover at Springer
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