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Probability: Theory and Examples, 4th  무료배송

 
지은이 : Rick Durrett
출판사 : Cambridge
판수 : 4 edition
페이지수 : 438
ISBN : 9780521765398
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 품절
     

 
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.

1. Measure theory
2. Laws of large numbers
3. Central limit theorems
4. Random walks
5. Martingales
6. Markov chains
7. Ergodic theorems
8. Brownian motion
Appendix A. Measure theory details.

"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."


"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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