Probabilistic Symmetries and Invariance Principles

Olav Kallenberg

ISBN 10: 0387251154 / ISBN 13: 9780387251158

Editore: Springer New York Jul 2005, 2005

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Neuware - 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's, the theory has evolved into a unique body of deep, beautiful, and often surprising results, comprising the basic representations and invariance properties in one and several dimensions, and exhibiting some unexpected links between the various symmetries as well as to many other areas of modern probability. Most chapters require only some basic, graduate level probability theory, and should be accessible to any serious researchers and graduate students in probability and statistics. Parts of the book may also be of interest to pure and applied mathematicians in other areas. The exposition is formally self-contained, with detailed references provided for any deeper facts from real analysis or probability used in the book. Olav Kallenberg received his Ph.D. in 1972 from Chalmers University in Gothenburg, Sweden. After teaching for many years at Swedish universities, he moved in 1985 to the US, where he is currently Professor of Mathematics at Auburn University. He is well known for his previous books Random Measures (4th edition, 1986) and Foundations of Modern Probability (2nd edition, 2002) and for numerous research papers in all areas of probability. In 1977, he was the second recipient ever of the prestigious Rollo Davidson Prize from Cambridge University. In 1991-94, he served as the Editor in Chief of Probability Theory and Related Fields. Professor Kallenberg is an elected fellow of the Institute of Mathematical Statistics.

Codice articolo 9780387251158

Dati bibliografici

• Titolo: Probabilistic Symmetries and Invariance Principles
• Editore: Springer New York Jul 2005
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 0387251154
• ISBN 13: 9780387251158
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 29 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 29 millimetri di profondità
• Peso: 500 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

Olav Kallenberg received his Ph.D. in 1972 from Chalmers University in Gothenburg, Sweden. After teaching for many years at Swedish universities, he moved in 1985 to the US, where he is currently Professor of Mathematics at Auburn University. He is well known for his previous books Random Measures (4th edition, 1986) and Foundations of Modern Probability (2nd edition, 2002) and for numerous research papers in all areas of probability. In 1977, he was the second recipient ever of the prestigious Rollo Davidson Prize from Cambridge University. In 1991–94, he served as the Editor in Chief of Probability Theory and Related Fields. Professor Kallenberg is an elected fellow of the Institute of Mathematical Statistics.