Stable Convergence and Stable Limit Theorems

• Main Authors: Häusler, Erich (Author), Luschgy, Harald (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Probability Theory and Stochastic Modelling, 74
• Subjects: Mathematics.; Probabilities.; Statistics.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.

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...

Table of Contents:

• 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.