© 2021

Foundations of Modern Probability

  • 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


Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 99)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Olav Kallenberg
    Pages 1-5
  3. Measure Theoretic Prerequisites

    1. Front Matter
      Pages 7-7
    2. Olav Kallenberg
      Pages 33-54
    3. Olav Kallenberg
      Pages 55-77
  4. Some Classical Probability Theory

    1. Front Matter
      Pages 79-79
    2. Olav Kallenberg
      Pages 81-99
    3. Olav Kallenberg
      Pages 101-123
    4. Olav Kallenberg
      Pages 125-146
    5. Olav Kallenberg
      Pages 147-160
  5. Conditioning and Martingales

    1. Front Matter
      Pages 161-161
    2. Olav Kallenberg
      Pages 163-183
    3. Olav Kallenberg
      Pages 185-206
    4. Olav Kallenberg
      Pages 207-229
  6. Markovian and Related Structures

    1. Front Matter
      Pages 231-231
    2. Olav Kallenberg
      Pages 233-253
    3. Olav Kallenberg
      Pages 255-276
    4. Olav Kallenberg
      Pages 277-294
  7. Some Fundamental Processes

    1. Front Matter
      Pages 295-295

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



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

Authors and affiliations

  1. 1.Department of Mathematics & StatisticsAuburn UniversityAuburnUSA

About the authors

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. 

Bibliographic information

  • Book Title Foundations of Modern Probability
  • Authors Olav Kallenberg
  • Series Title Probability Theory and Stochastic Modelling
  • Series Abbreviated Title Probability and Stochastic (formerly: PIA & SMAP)
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2021
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-030-61870-4
  • Softcover ISBN 978-3-030-61873-5
  • eBook ISBN 978-3-030-61871-1
  • Series ISSN 2199-3130
  • Series E-ISSN 2199-3149
  • Edition Number 3
  • Number of Pages XII, 946
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site