Foundations of modern probability. 2nd ed.

*(English)*Zbl 0996.60001
Probability and Its Applications. New York, NY: Springer. xvii, 638 p. (2002).

This second edition presents now even more material in the concise and elegant style of the former edition (1997; Zbl 0892.60001) which by now has become a highly praised standard reference book for many areas of probability theory. The new topics are mainly concerned with asymptotics of Markov processes (e.g., more general ergodic theorems, Palm distributions, entropy, Harris recurrence) and with fundamental large deviation theory. Moreover, the inclusion of a second chapter on measure theory makes the book now almost self-contained. The chapters of the first edition have been carefully revised and corrected so that it has become an even more accurate and reliable reference work. Starting a book with a page entitled “Praise for the first edition” is always daring, but in the case of Kallenberg’s treatise indeed justified. The patient reader is waiting for further topics covered by the author in the years to come.

Reviewer: Markus Reiß (Berlin)