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Probability: Theory and Examples (Cambridge Series in Statistical and Probabilistic Mathematics) Hardcover – August 30, 2010

ISBN-13: 978-0521765398 ISBN-10: 0521765390 Edition: 4th

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Product Details

  • Series: Cambridge Series in Statistical and Probabilistic Mathematics
  • Hardcover: 438 pages
  • Publisher: Cambridge University Press; 4 edition (August 30, 2010)
  • Language: English
  • ISBN-10: 0521765390
  • ISBN-13: 978-0521765398
  • Product Dimensions: 8.5 x 1.1 x 10 inches
  • Shipping Weight: 2.1 pounds (View shipping rates and policies)
  • Average Customer Review: 2.9 out of 5 stars  See all reviews (31 customer reviews)
  • Amazon Best Sellers Rank: #238,678 in Books (See Top 100 in Books)

Editorial Reviews

Review

"This book is also an excellent resource. Several interesting and concrete examples are presented throughout the textbook, which will help novices obtain a better understanding of the fundamentals of probability theory."
Ramesh Garimella, Computing Reviews

"The best feature of the book is its selection of examples. The author has done an extraordinary job in showing not simply what the presented theorems can be used for, but also what they cannot be used for."
Miklos Bona, SIGACT News

Book Description

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The new edition begins with a short chapter on measure theory to orient readers new to the subject.

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Customer Reviews

I can only second the statements made by others that Durrett's book is overly terse and the organization confusing.
Robert I. Mccaw
While attempting various homework problems or reading the text, I often find that I would like clarification on the specifics of a definition.
Anonymous
Being done with the class, I now find the book an excellent reference - it is a very concise presentation of the material.
D. Martin

Most Helpful Customer Reviews

22 of 24 people found the following review helpful By Fab on April 3, 2005
Format: Hardcover
As someone pointed out, once you have understood the material, Durrett's Text is a good reference that collects an awful lot of material very concisely (though in an uncommon arrangement). But many proofs are just too terse. Often things are implied, but not spelled out.
This text really forces you to do your own work, which can be very rewarding, but also very frustrating.

Note that many of the positive reviews seem to come from lecturers, and note also that in many US universities the lecturer effectively chooses the text, not the students, which might explain the "success" of the book despite its flaws (not to mention the high price).

To conclude, I found myself always reading other books (eg. Williams, Billingsley) to find out what was going on, and even then sometimes had difficulties following Durrett's exposition and proofs. Would not recommend the text unless it is required, or for reference.
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25 of 28 people found the following review helpful By Machine Learning Researcher on September 8, 2004
Format: Hardcover
The book has a nice collection of topics, perhaps the nicest and most modern one out of the usual textbooks out there. Unfortunately, it is poorly written. The proofs of theorems are extremely unclear, even after thinking about them for some time. Furthermore, the notation is not standard and since not all of it is in the nice list at the end, I find myself often looking through the book for an explanation of some piece of notation.

My experience is with the brand new third edition. It seems that the only changes are correction of errors, cheaper price and some minor correnctions. However, I still found some errors after a short inspection and also some that I suspect, but not sure that are errors.

My advice is do not be tempted by the nice modern table of contents and by the late publication date (2005 for the third edition). I guess we have to stick to the other older texts on the topic. I strongly recommend Williams' Probability with Martingales or Ash's second edition Probability and Measure over this book.
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35 of 41 people found the following review helpful By Anonymous on November 21, 2005
Format: Hardcover
While attempting various homework problems or reading the text, I often find that I would like clarification on the specifics of a definition. Almost invariably, the index does not contain a reference to the material I need.

Here's an example:

Let's say I want to do exercise 6.8 on page 51, which involves the Poisson distribution. I want to have the precise definition of a Poisson distribution (this information can be found on pages 19 and 91). I look under "Poisson" in the index and find:

Poisson approximation 36

Poisson convergence 135

Poisson process 143, 147, 150

Because the exercise is on page 51, it seems that Poisson approximation on page 36 is my best bet. On page 36 I cannot find a single occurrence of "Poisson," though I do see "Polynomial approximation."
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32 of 39 people found the following review helpful By A Customer on May 20, 2001
Format: Hardcover
While the book is modern, in the sense that it includes a few new proofs of standard results, I find it extremely hard to follow. While Durrett has tried to order things in a nice way, and introduce things as he goes along he has overdone it. Proofs are extremely hard to follow / except for the trivial ones/. Even some of the easy proofs, are written in such a way that a ten minute proof may turn into a 2 hour nightmare of follow-ups to other examples as well as referral to exercises which are not trivial at all to prove, but without which you cannot understand the proof completely. In general, the book is extremely painful to go through, so unless you have Feller's books and Shiryaev on the side, be prepared for quite a bit of frustration. As far as reference book, this also the wrong to buy, unless you have read and solved each exercise as you go along, you can never understand a proof. So, if you need as self-contained proof on Markov Chains, this is not the book to use. The usual mistakes and typos exist here as well, just like in any math book, but the problem is that referring to the wrong exercises to supplement you proof may discourage any reader from following through. / also at times the logic seems to be weird, like stating and if result but using it as the only if part of it, or vice versa/ In general, I would not recommend this book and considering the price of $114/ what are these people thinking?/ it is almost a stupidy to buy, unless you have to.
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30 of 39 people found the following review helpful By Giuseppe A. Paleologo on February 6, 1998
Format: Hardcover
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.
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