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Stable convergence and stable limit ...

Hausler, Erich.

Stable convergence and stable limit theorems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stable convergence and stable limit theoremsby Erich Hausler, Harald Luschgy.
Author:	Hausler, Erich.
other author:	Luschgy, Harald.
Published:	Cham :Springer International Publishing :2015.
Description:	x, 228 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Limit theorems (Probability theory)
Online resource:	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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100 1 $a Hausler, Erich. $3 726886
245 1 0 $a Stable convergence and stable limit theorems $h [electronic resource] / $c by Erich Hausler, Harald Luschgy.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a x, 228 p. : $b ill., digital ; $c 24 cm.
490 1 $a Probability theory and stochastic modelling, $x 2199-3130 ; $v v.74
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.
650 0 $a Limit theorems (Probability theory) $3 182695
650 0 $a Convergence. $3 182684
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Statistical Theory and Methods. $3 274054
700 1 $a Luschgy, Harald. $3 468023
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Probability theory and stochastic modelling ; $v v.70. $3 683306
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-18329-9
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