Probabilistic Symmetries and Invariance Principles

• Main Author: Kallenberg, Olav (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2005.
• Series: Probability and Its Applications,
• Subjects: Statistics.; Probabilities.; Statistical Theory and Methods.; Probability Theory and Stochastic Processes.

This is the first comprehensive treatment of the three basic symmetries of probability theory—contractability, exchangeability, and rotatability—defined as invariance in distribution under contractions, permutations, and rotations. Originating with the pioneering work of de Finetti from the 1930...

Table of Contents:

• The Basic Symmetries
• Conditioning and Martingales
• Convergence and Approximation
• Predictable Sampling and Mapping
• Decoupling Identities
• Homogeneity and Reflections
• Symmetric Arrays
• Multi-variate Rotations
• Symmetric Measures in the Plane.