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Stable convergence and stable limit ...

Hausler, Erich.

Stable convergence and stable limit theorems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Stable convergence and stable limit theoremsby Erich Hausler, Harald Luschgy.
作者:	Hausler, Erich.
其他作者:	Luschgy, Harald.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	x, 228 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Limit theorems (Probability theory)
電子資源:	http://dx.doi.org/10.1007/978-3-319-18329-9
ISBN:	9783319183299 (electronic bk.)

Stable convergence and stable limit theorems
Hausler, Erich.

Stable convergence and stable limit theorems[electronic resource] /by Erich Hausler, Harald Luschgy. - Cham :Springer International Publishing :2015. - x, 228 p. :ill., digital ;24 cm. - Probability theory and stochastic modelling,v.742199-3130 ;. - Probability theory and stochastic modelling ;v.70..

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.

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.

ISBN: 9783319183299 (electronic bk.)

Standard No.: 10.1007/978-3-319-18329-9doiSubjects--Topical Terms:

182695
Limit theorems (Probability theory)

LC Class. No.: QA273.67 / .H38 2015

Dewey Class. No.: 519.2

Stable convergence and stable limit theorems
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505 0 $a 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.
520 $a 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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