Probability: Theory and Examples

I used this for self-study while doing a post-doc in applied mathematics. I completed 90% of it and am very glad that I did. Topics are motivated well and the proofs are clear. The book is concise enough that it makes a good reference--however, the organization isn't as suited for a reference as say Loeve's texts. It is written at the same level as a graduate text in real analysis.

To quote professor Durrett: "Probability: Theory and Examples is written for a graduate course in probability. It is not designed for undergraduates or others who are learning the material for the first time. At the graduate level it has been very successful and is one of the mostly commonly used texts in the country. A third edition with more typos corrected and hopefully a lower price will come in roughly October 2003." Indeed, in order to begin with chapter 1, you need a solid foundation in analysis and abstract measure theory. (You can actually read the book without this background, but then you would need to start with the material in the appendices and then go to chapter 1. However, appendices are often meant for refreshing of filling in the gaps of lost knowledge.) For a graduate student with the proper background, there are few probability books that compare. Many journey too readily into the abstraction of sigma fields, for example. And this, I believe, is why Durrett's book is well respected. He really does stick to concrete examples, and avoids being so abstract as to become incomprehensible. In fact, to be more understandable, his statements are often short and to the point. Such writing style may take adjustment for the reader, and you will have to fill in details yourself, but such a method of reading is standard for many math textbooks. Surely this edition is imperfect (sometimes spotty index, occasional statements which are hard to follow), but on the whole the text is very well written, insightful and understandable for the appropriate audience. The upcoming fourth edition should improve on the imperfections mentioned above.

I took a grad class in Probability, and we used this book. I would not have followed the proofs from the book alone, but following the instructor's presentation, it went along just fine. The book has very good exercises that often make you use several of the recently presented ideas in a single question. Being done with the class, I now find the book an excellent reference - it is a very concise presentation of the material. I recommend this book if you're a student in a graduate-level class or if you're already familiar with the material. But if you want to teach yourself, this book is too difficult a starting point.

I used the book as one of the main sources for a two semester course in probability. Besides its special style, which you may or may not like (I do), it covers a wide range of modern topics and is thus one of the best books in probability for graduate students (and researchers :-) ).

Apparently, the perfect text of probability has not been written yet. Durrett's textbook is as good as other good textbooks (there are not many around), but has still some flaws. Some topics (martingales, brownian motion) are given relatively more attention than in other popular textbooks, say Billingsley's "Probability and Measure". In general, the choice of the topics and their organization is what differentiates this textbook and makes it valuable. The style is somewhat terse, and sometimes the reader would appreciate some wrds of advice about the relative importance of topics and techniques (see for example the very readable "Probability with Martingales" by Williams). The problems are interesting. The book is very useful when used jointly with other, possibly more wordy, references. This edition has less typos then the first (which was an editorial scandal), but still too many to be considered decent. With less typos and a few more explanations, the third edition has good chances to become "the" reference textbook for probabilists.