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Stable Convergence and Stable Limit Theorems

  • Erich Häusler
  • Harald Luschgy

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 74)

Table of contents

  1. Front Matter
    Pages i-x
  2. Erich Häusler, Harald Luschgy
    Pages 1-9
  3. Erich Häusler, Harald Luschgy
    Pages 11-19
  4. Erich Häusler, Harald Luschgy
    Pages 21-37
  5. Erich Häusler, Harald Luschgy
    Pages 39-53
  6. Erich Häusler, Harald Luschgy
    Pages 55-65
  7. Erich Häusler, Harald Luschgy
    Pages 67-122
  8. Erich Häusler, Harald Luschgy
    Pages 123-144
  9. Erich Häusler, Harald Luschgy
    Pages 145-158
  10. Erich Häusler, Harald Luschgy
    Pages 159-172
  11. Erich Häusler, Harald Luschgy
    Pages 173-186
  12. Back Matter
    Pages 187-228

About this book

Introduction

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.

Keywords

60-02, 60F05, 60F17 Gauss kernels limit theorems mixing convergence of random variables stable convergence of random variables weak convergence of Markov kernels

Authors and affiliations

  • Erich Häusler
    • 1
  • Harald Luschgy
    • 2
  1. 1.Mathematical InstituteUniversity of GiessenGiessenGermany
  2. 2.University of TrierTrierGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-18329-9
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-18328-2
  • Online ISBN 978-3-319-18329-9
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
  • Buy this book on publisher's site