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Stable convergence and stable limit theorems / Erich Hausler and Harald Luschgy.

By: Contributor(s): Series: Probability theory and stochastic modelling ; 74.Publication details: Cham : Springer, 2015.Description: x, 228 p. ; 24 cmISBN:
  • 9783319183282
Subject(s): DDC classification:
  • 519.2 23 H376
Contents:
1. Why stable convergence? -- 2. Weak convergence of Markov Kernels -- 3. Stable convergence of random variables -- 4. Applications -- 5. Stability of limit theorems -- 6. Stable Martingale central limit theorems -- 7. Stable functional Martingale central limit theorems -- 8. A stable limit theorem with exponential rate -- 9. Autoregression of order one -- 10. Galton-Watson branching processes -- Appendix A -- Appendix B -- Abbreviations of formulas -- Notation index -- References -- Index.
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 Renyi, 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 at the master's level with a solid knowledge of measure theoretic probability.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 519.2 H376 (Browse shelf(Opens below)) Available 137127
Total holds: 0

Includes bibliographical references and index.

1. Why stable convergence? --
2. Weak convergence of Markov Kernels --
3. Stable convergence of random variables --
4. Applications --
5. Stability of limit theorems --
6. Stable Martingale central limit theorems --
7. Stable functional Martingale central limit theorems --
8. A stable limit theorem with exponential rate --
9. Autoregression of order one --
10. Galton-Watson branching processes --
Appendix A --
Appendix B --
Abbreviations of formulas --
Notation index --
References --
Index.

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 Renyi, 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 at the master's level with a solid knowledge of measure theoretic probability.

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