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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.

Probabilities. --- Symmetry (Physics) --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Invariance principles (Physics) --- Symmetry (Chemistry) --- Conservation laws (Physics) --- Physics --- Mathematical statistics. --- Distribution (Probability theory. --- Statistical Theory and Methods. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Statistical methods --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics

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From the reviews of the first editions: "... Kallenberg's present book would have to qualify as the assimilation of probability par excellence. It is a great edifice of material, clearly and ingeniously presented, without any non-mathematical distractions. Readers wishing to venture into it may do so with confidence that they are in very capable hands." F.B. Knight, Mathematical Reviews "...Indeed the monograph has the potential to become a (possibly even "the") major reference book on large parts of probability theory for the next decade or more." M. Scheutzow, Zentralblatt "The theory of probability has grown exponentially during the second half of the twentieth century and the idea of writing a single volume that could serve as a general reference for much of the modern theory seems almost foolhardy. Yet this is precisely what Professor Kallenberg has attempted in the volume under review and he has accomplished it brilliantly...It is astonishing that a single volume of just over five hundred pages could contain so much material presented with complete rigor and still be at least formally self-contained..." R.K. Getoor, Metrika This new edition contains four new chapters as well as numerous improvements throughout the text. Olav Kallenberg was educated in Sweden, where he received his Ph.D. in 1972 from Chalmers University. After teaching for many years at Swedish universities, he moved in 1985 to the U.S., where he is currently a Professor of Mathematics at Auburn University. He is known for his book "Random Measures" (4th edition, 1986) 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.".

Stochastic processes --- AA / International- internationaal --- 303.3 --- Waarschijnlijkheid. Probabiliteit. Nauwkeurigheid. Residuals: measurement and specification (wiskundige statistiek). --- Probabilities. --- Topology. --- Probability Theory and Stochastic Processes. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Waarschijnlijkheid. Probabiliteit. Nauwkeurigheid. Residuals: measurement and specification (wiskundige statistiek)

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From the reviews of the first edition: "... To sum it up, one can perhaps see a distinction among advanced probability books into those which are original and path-breaking in content, such as Levy's and Doob's well-known examples, and those which aim primarily to assimilate known material, such as Loeve's and more recently Rogers and Williams'. Seen in this light, Kallenberg's present book would have to qualify as the assimilation of probability par excellence. It is a great edifice of material, clearly and ingeniously presented, without any non-mathematical distractions. Readers wishing to venture into it may do so with confidence that they are in very capable hands." Mathematical Reviews "... Indeed the monograph has the potential to become a (possibly even ``the'') major reference book on large parts of probability theory for the next decade or more." Zentralblatt "The theory of probability has grown exponentially during the second half of the twentieth century and the idea of writing a single volume that could serve as a general reference for much of the modern theory seems almost foolhardy. Yet this is precisely what Professor Kallenberg has attempted in the volume under review and he has accomplished it brilliantly. ... It is astonishing that a single volume of just over five hundred pages could contain so much material presented with complete rigor and still be at least formally self- contained. ..." Metrica This new edition contains four new chapters as well as numerous improvements throughout the text.

Probabilities --- Stochastic processes --- Probabilities. --- Probabilités --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- Probability Theory and Stochastic Processes. --- Distribution (Probability theory. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk

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This new, thoroughly revised and expanded 3rd edition of a classic gives a comprehensive coverage of modern probability in a single book. It is a truly modern text, providing not only classical results but also material that will be important for future research. Much has been added to the previous edition, including eight entirely new chapters on subjects like random measures, Malliavin calculus, multivariate arrays, and stochastic differential geometry. Apart from important improvements and revisions, some of the earlier chapters have been entirely rewritten. To help the reader, the material has been grouped together into ten major areas, each arguably indispensable to any serious graduate student and researcher, regardless of their specialization. Each chapter is largely self-contained and includes plenty of exercises, making the book ideal for self-study and for designing graduate-level courses and seminars in different areas and at different levels. Extensive notes and a detailed bibliography make it easy to go beyond the presented material if desired. From the reviews of the first edition: “…readers are likely to regard the book as an ideal reference. Indeed the monograph has the potential to become a (possibly even “the”) major reference book on large parts of probability theory for the next decade or more.” M. Scheutzow, zbMATH “…great edifice of material, clearly and ingeniously presented, without any non-mathematical distractions. Readers … are in very capable hands.” F. B. Knight, Mathemtical Reviews “… this is precisely what Professor Kallenberg has attempted … and he has accomplished it brilliantly... It is astonishing that a single volume of just over five hundred pages could contain so much material presented with complete rigor and still be at least formally self-contained..." R.K. Getoor, Metrika From the reviews of the second edition: “This … edition presents … more material in the concise and elegant style of the former edition which by now has become a highly praised standard reference book for many areas of probability theory.” M. Reiß, zbMATH “… the … monograph is a modern classic in probability theory… …every … expert in one of the various topics covered by this monograph will reconsider his own point of view and gain deeper insight into his subject.” Klaus D. Schmidt, Mathematical Reviews .

Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Probability Theory.

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Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.

Operational research. Game theory --- Probability theory --- waarschijnlijkheidstheorie --- stochastische analyse --- kansrekening