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Stable convergence and stable limit theorems

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 p...

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Detalles Bibliográficos
Autores principales: Häusler, Erich, Luschgy, Harald
Lenguaje:eng
Publicado: Springer 2015
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-18329-9
http://cds.cern.ch/record/2032372
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author Häusler, Erich
Luschgy, Harald
author_facet Häusler, Erich
Luschgy, Harald
author_sort Häusler, Erich
collection CERN
description 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 at the master's level with a solid knowledge of measure theoretic probability.
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spelling cern-20323722021-04-21T20:09:56Zdoi:10.1007/978-3-319-18329-9http://cds.cern.ch/record/2032372engHäusler, ErichLuschgy, HaraldStable convergence and stable limit theoremsMathematical Physics and MathematicsThe 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 at the master's level with a solid knowledge of measure theoretic probability.Springeroai:cds.cern.ch:20323722015
spellingShingle Mathematical Physics and Mathematics
Häusler, Erich
Luschgy, Harald
Stable convergence and stable limit theorems
title Stable convergence and stable limit theorems
title_full Stable convergence and stable limit theorems
title_fullStr Stable convergence and stable limit theorems
title_full_unstemmed Stable convergence and stable limit theorems
title_short Stable convergence and stable limit theorems
title_sort stable convergence and stable limit theorems
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-18329-9
http://cds.cern.ch/record/2032372
work_keys_str_mv AT hauslererich stableconvergenceandstablelimittheorems
AT luschgyharald stableconvergenceandstablelimittheorems