Probabilistic Symmetries and Invariance Principles

Name: Probabilistic Symmetries and Invariance Principles
Brand: Springer, Berlin
SKU: 9781441920423
Price: 732.44 RON
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Autor: Olav Kallenberg

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Editura: Springer, Berlin

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This book is about random objects sequences, processes, arrays, measures, functionals with interesti...

Informații despre carte

Autor

Olav Kallenberg

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2010

Pagini

512

EAN

9781441920423

ISBN

1441920420

Enbook ID

02716939

Editura

Springer, Berlin

Greutate

785

Dimensiuni

155 x 235 x 26

Descriere completă

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.

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