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Stable Convergence and Stable Limit Theorems / by Erich Häusler, Harald Luschgy.
Springer Nature - Springer Mathematics and Statistics eBooks 2015 English International Available online
View online- Format:
- Book
- Author/Creator:
- Häusler, Erich., Author.
- Luschgy, Harald., Author.
- Series:
- Probability Theory and Stochastic Modelling, 2199-3149 ; 74
- Language:
- English
- Subjects (All):
- Probabilities.
- Statistics.
- Probability Theory.
- Statistical Theory and Methods.
- Local Subjects:
- Probability Theory.
- Statistical Theory and Methods.
- Physical Description:
- 1 online resource (231 p.)
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2015.
- Language Note:
- English
- Summary:
- The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students atthe master's level with a solid knowledge of measure theoretic probability.
- Contents:
- Preface
- 1.Weak Convergence of Markov Kernels
- 2.Stable Convergence
- 3.Applications
- 4.Stability of Limit Theorems
- 5.Stable Martingale Central Limit Theorems
- 6.Stable Functional Martingale Central Limit Theorems
- 7.A Stable Limit Theorem with Exponential Rate
- 8.Autoregression of Order One
- 9.Branching Processes
- A. Appendix
- B. Appendix
- Bibliography.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references and index.
- ISBN:
- 3-319-18329-X
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