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Cambridge Series in Statistical and Probabilistic Mathematics #31
Probability: Theory and Examples
This book is an introduction to probability theory covering 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.
- GenresMathematicsTextbooks
440 pages, Hardcover
First published August 30, 2010
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Displaying 1 - 3 of 3 reviews
June 19, 2014
Good book full of helpful examples and exercises. I used this for a class along with Probability & Measure Theory and they complement each other well. We used this one more later in the course, since it covers less of the underlying measure theory but has more interesting examples in probability theory as such.
Some of the notation was a bit nonstandard (compared to the other book and our course notes) but still fairly easy to follow.
Some of the notation was a bit nonstandard (compared to the other book and our course notes) but still fairly easy to follow.
August 29, 2018
Something that took me a while to understand, mainly because I had given up on reading this book, is that to read it, you should already have had a measure theory course. In fact it's mandatory. Simple theorems - I don't remember well, but I think an example of those was \int h(x) dF_X = \int h(x) f_X dx, when a the dist. has a density - are not in the 1st chapter, and are constantly used beyond it. Here lies the major problem with the book. The author was lazy, put forth the appendix as a chapter, and didn't informed the reader of the requirements to really understand the book. This shows, since some of the notation used in the 1st chapter is not defined in it, but only in chapter 2, or later.
However, this is not the only example of lazzyness from the author. Another example is the example 3.6.8 for the definition of a poisson process on a measure space... You don't know to which sigma-algebra the sets belong to, everything is so condensed in to prose-like text that I prefered to just check the wikipedia page (Poisson Random Measure). The whole book is sprinkled with examples where the author could have done a better job at being more explicit, and using less irony. I would be ashamed if, in most examples, wikipedia did a better job. Some writing is so extempore/blunt, that it really makes one wonder how he's a professor. In exercise 4.4.3, there's this sentence about renewal process and the arrival times of what could be considered as costumers: «(Think of a public telephone or prostitute)». What's the relevance of the last example? It sounded to me so ridiculous and 'dislocated' as him writing «Think of a gas chamber». Honestly...
The big risk is that if you're using this book for self-study, there's confounding between lazy writing, irony (which is often used by the author), and typos... The non-native reader has increased difficulty in separating whether what's unclear, and what's simply a typo. Many times simply wasting his/her time when they could be reading something more fulfilling. Honestly I find the books by Resnick much more complete, and useful.
The worst part are the proofs, since in those the author really summarises everything to a bare minimum. And again, I had to complement sometimes with wikipedia, which does a much better job. The best way to read this book is to just get a general idea of the 'forest' which is probability theory, and then pick up another book for the 'trees'... Don't worry too much with the proofs in Durrett's, skim them, do the exercises with the errata next to you, and then just move on with your life.
After all these years, I maintain my score to 1 star. The amount of time lost on the book, was not fun...
However, this is not the only example of lazzyness from the author. Another example is the example 3.6.8 for the definition of a poisson process on a measure space... You don't know to which sigma-algebra the sets belong to, everything is so condensed in to prose-like text that I prefered to just check the wikipedia page (Poisson Random Measure). The whole book is sprinkled with examples where the author could have done a better job at being more explicit, and using less irony. I would be ashamed if, in most examples, wikipedia did a better job. Some writing is so extempore/blunt, that it really makes one wonder how he's a professor. In exercise 4.4.3, there's this sentence about renewal process and the arrival times of what could be considered as costumers: «(Think of a public telephone or prostitute)». What's the relevance of the last example? It sounded to me so ridiculous and 'dislocated' as him writing «Think of a gas chamber». Honestly...
The big risk is that if you're using this book for self-study, there's confounding between lazy writing, irony (which is often used by the author), and typos... The non-native reader has increased difficulty in separating whether what's unclear, and what's simply a typo. Many times simply wasting his/her time when they could be reading something more fulfilling. Honestly I find the books by Resnick much more complete, and useful.
The worst part are the proofs, since in those the author really summarises everything to a bare minimum. And again, I had to complement sometimes with wikipedia, which does a much better job. The best way to read this book is to just get a general idea of the 'forest' which is probability theory, and then pick up another book for the 'trees'... Don't worry too much with the proofs in Durrett's, skim them, do the exercises with the errata next to you, and then just move on with your life.
After all these years, I maintain my score to 1 star. The amount of time lost on the book, was not fun...
March 25, 2017
Pros:
1. Classical and widely used textbook for graduate students
2. Clear structure. Divide probability theory into Large Number Law, Central Limit Theorem, Random Walk, Martingales, Markov Chains, Ergodic Theorems and Brownian Motion, which covers important basic topics in graduate probability theory.
Cons:
1. Some typos
2. Students use 4th edition while some professors may use 3rd edition. It is a bit annoying.
3. Some proofs and explanations are not easy to understand
1. Classical and widely used textbook for graduate students
2. Clear structure. Divide probability theory into Large Number Law, Central Limit Theorem, Random Walk, Martingales, Markov Chains, Ergodic Theorems and Brownian Motion, which covers important basic topics in graduate probability theory.
Cons:
1. Some typos
2. Students use 4th edition while some professors may use 3rd edition. It is a bit annoying.
3. Some proofs and explanations are not easy to understand
Displaying 1 - 3 of 3 reviews