
Foundations of Modern Probability
Prof. Olav Kallenberg in Probability Theory and Stochastic Modelling (2021)
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新版《概率论》第三版经过了彻底的修订和扩充，在一本书中对现代概率进行了全面的阐述。它是一个真正的现代阐述版，不仅提供经典的结果，而且材料，将是重要的未来研究。很多已经添加到以前的版本，包括8个全新的章节，随机度量，Malliavin 微积分，多元数组，和随机微分几何。除了重要的改进和修订，一些早期章节已经被完全重写。为了帮助读者，这些材料被分为十个主要领域，每一个领域对于任何严肃的研究生和研究者来说都是必不可少的，无论他们的专业是什么。
每一章很大程度上是独立的，包括大量的练习，使书理想的自学和设计研究生水平的课程和研讨会在不同的领域和不同的水平。广泛的注释和详细的参考书目使它很容易超越所提出的材料，如果需要。
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From the Back Cover
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 selfcontained and includes plenty of exercises, making the book ideal for selfstudy and for designing graduatelevel 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 nonmathematical 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 selfcontained..." 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
About the Author
Olav Kallenberg (Ph.D., Chalmers University, Gothenburg, Sweden, 1972) is an Emeritus Professor at Auburn University. He has held research positions in Sweden and abroad and taught in the US for more than 30 years. In 1977 he was awarded the Rollo Davidson Prize by Cambridge University, in 1989 he was elected a Fellow of the IMS, and in 1991–94 he served as the editor of PTRF. He has given plenary talks at major conferences all over the world, and was the opening lecturer at both the Vilnius Conference in 2006 and at the SPA Conference in Gothenburg in 2018. Apart from his numerous research papers, he is known for his Springer books Probabilistic Symmetries and Invariance Principles (2005) and Random Measures, Theory and Applications (2017). His book Foundations of Modern Probability (1997, 2002, and 2021) has become a classic reference work.

