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Stable convergence and stable limit theorems [electronic resource] / Erich Häusler, Harald Luschgy.

9783319183299 electronic book
331918329X electronic book
9783319183282

Cham : Springer, 2015.

English

1 online resource.

QA273.67

519.2

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.

Includes bibliographical references and index.

Access limited to authorized users.

Online resource; title from PDF title page (viewed June 15, 2015).

Probability theory and stochastic modelling ; v. 74.

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