Probabilistic Symmetries and Invariance Principles (Paperback, Softcover reprint of hardcover 1st ed. 2005)

This book is about random objects-sequences, processes, arrays, measures, functionals-with interesting symmetry properties. Here symmetry should beunderstoodinthebroadsenseofinvarianceunderafamily(notnecessarily a group) of measurable transformations. To be precise, it is not the random objects themselves but rather their distributions that are assumed to be symmetric. Though many probabilistic symmetries are conceivable and have been considered in various contexts, four of them-stationarity, contractability, exchangeability, and rotatability-stand out as especially interesting and - portant in several ways: Their study leads to some deep structural theorems of great beauty and signi?cance, they are intimately related to some basic areasofmodernprobabilitytheory, andtheyaremutuallyconnectedthrough a variety of basic relationships. The mentioned symmetries may be de?ned as invariance in distribution under shifts, contractions, permutations, and rotations. Stationarity being a familiar classical topic, treated extensively in many standard textbooks and monographs, most of our attention will be focused on the remaining three basic symmetries. The study of general probabilistic symmetries essentially originated with the work of de Finetti (1929-30), who proved by elementary means (no - vanced tools being yet available) the celebrated theorem named after him- the fact that every in?nite sequence of exchangeable events is mixed i.i.d.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Probability and Its Applications
Release date:	December 2010
First published:	2005
Authors:	Olav Kallenberg
Dimensions:	235 x 155 x 26mm (L x W x T)
Format:	Paperback
Pages:	512
Edition:	Softcover reprint of hardcover 1st ed. 2005
ISBN-13:	978-1-4419-2042-3
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Promotions
LSN:	1-4419-2042-0
Barcode:	9781441920423

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