# Stable Convergence and Stable Limit Theorems

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

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

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.

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

- 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
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