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Concentration inequalities for sums and martingales / by Bernard Bercu, Bernard Delyon, Emmanuel Rio.
Springer Nature - Springer Mathematics and Statistics eBooks 2015 English International Available online
View online- Format:
- Book
- Author/Creator:
- Bercu, Bernard, Author.
- Delyon, Bernard., Author.
- Rio, Emmanuel., Author.
- Series:
- SpringerBriefs in Mathematics, 2191-8198
- Language:
- English
- Subjects (All):
- Probabilities.
- Mathematics.
- History.
- Functions of complex variables.
- Probability Theory and Stochastic Processes.
- History of Mathematical Sciences.
- Several Complex Variables and Analytic Spaces.
- Local Subjects:
- Probability Theory and Stochastic Processes.
- History of Mathematical Sciences.
- Several Complex Variables and Analytic Spaces.
- Physical Description:
- 1 online resource (131 p.)
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2015.
- Language Note:
- English
- 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.
- Contents:
- Classical Results
- Concentration Inequalities for Sums
- Concentration Inequalities for Martingales
- Applications in Probability and Statistics.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references at the end of each chapters.
- ISBN:
- 3-319-22099-3
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