Authors:
- Due to its size, and for the convenience of the reader, the print version of this book come in two separate volumes
- Presents a unified treatment of probability theory in a thoroughly revised and substantially extended 3rd edition of this classic text
- Invites the reader to go beyond the presented material via its extensive notes and detailed bibliography
- Includes supplementary material: sn.pub/extras
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 99)
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Table of contents (36 chapters)
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Front Matter
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Measure Theoretic Prerequisites
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Front Matter
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Some Classical Probability Theory
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Front Matter
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Conditioning and Martingales
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Front Matter
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Markovian and Related Structures
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Front Matter
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Some Fundamental Processes
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Front Matter
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About this book
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
Keywords
- 60-00, 60-01, 60A10, 60G05
- conditioning and martingales
- measure-theoretic foundations
- classical limit theorems
- Markov chains and processes
- Brownian Motion
- Brownian motion and Poisson processes
- stochastic calculus and applications
- stationarity and invariance
- random sets and measures
- SDEs and potential theory
- reference work on Probability
Reviews
“The book under review is the magnum opus of a brilliant scholar of probability. … An important feature of the book … is the writing style. … The choice of topics is excellent, some of which are not covered elsewhere. This book would make an outstanding text for graduate courses in measure theoretic probability, and for graduate students and faculty doing research in probability. The book is a delight to read. Highly recommended.” (Myron Hlynka, Mathematical Reviews, April, 2022)
Authors and Affiliations
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Department of Mathematics & Statistics, Auburn University, Auburn, USA
Olav Kallenberg
About the author
Bibliographic Information
Book Title: Foundations of Modern Probability
Authors: Olav Kallenberg
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-030-61871-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-61870-4Published: 08 February 2021
Softcover ISBN: 978-3-030-61873-5Published: 08 February 2022
eBook ISBN: 978-3-030-61871-1Published: 07 February 2021
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 3
Number of Pages: XII, 946
Number of Illustrations: 1 b/w illustrations