A Course in Probability Theory, Third Edition

I bought this book a long time ago and I had to brush up on some math before I dove in. I used this a self-study and it was a winner.Where this book really shines is the structure of the text and the authors writing style.Each chapter he starts with the high level, and theorems with proofs, and examples. Then he progresses deeper into the topic with both more advanced theorems, and applications.My only real complaint is that he could use a few more examples and exercises.Otherwise the author did a great job creating an inuitive and cohesive textbook.Once you have the math background, this is an excellent book.

I think Chung's book is an essential tool for learning to attack basic problem of probability theory. I dislike a little bit this book because the author is sometimes too much arrogant and his star/selected exercises aren't the most difficult (so, there is no guide in chosing exercises to solve).

I received the book in very good quality and promptly. I recommend this bookstore.

Classical but not easy to read.

There are several nice books in Grad-level Probability Theory. Billingsley's "Probability and Measure" is the richest one, but somehow poor organized and unpleasant printing. Resnick's "Probability Path" serve best for those who has no time to prepare first in measure theory and Lebesque integration but sacrifice some detail in latter part of the book. If you don't have previous Real Analysis training, I would suggest read Resnick first, and then find Billingsley for reference. But if you already good at measure and integration, Kai Lai Chung's "A Course in Probability Theory" still the best textbook teach step by step without losing detail. Chung's style is friendly to self studying like Resnick, but cover more detail in latter part of the book than Resnick. Chung's book is the best companion fot typical one semester course regradless what textbook your teacher choose. In the other words , Resnick helps students significantly in first half of the semester, Chung helps in the whole semester, and Billingsley may offer best effort after you took the Probability Theory course.

I read Billingsley and Ross for probability long time ago. After years of rust of my brain, I needed to review probability before I read about stochastic calculus. But, I didn't want to go through small typesets of thick Billingsley's. And Ross' book was rather elementary for measure theoretic stochastic calculus.Chung's book was an excellent choice for me, as it was compact yet rigorous. Every theorem was clear and easy to understand. The topics were nice and well organized in good order.In fact, it is preferable to have this book at hand if you want to read "Brownian motion and stochastic calculus" by Karatzas & Shreve as they refer theorems in Chung's book for details.

This book assumes that you have a certain degree of mathematical maturity, but gives you very thorough proofs of the basic concepts of rigorous probability. There is no hand waving here. You are expected to have followed an introduction to measure theory. Don't expect to go through this book in a term, but when you have finished it you will be able to consider yourself to be able to come up with proofs like a mathematician. In other words it will leave you with solid foundations.I can not imagine this book being used as an introduction.When you are finished you should be ready for a book like  Foundations of Modern Probability .

The book is extremely well organized, it contains everything important about Advanced Probability. The proofs for various versions of the Law of Large Numbers and Central Limit Theorems are amazing. And almost all math proofs in this book are quite detailed to understand (better than Feller's II volume). The newly added appendix "Measure and Integral" in 3rd edition turns to be very useful and it contains some useful results that I can't even find at the same detailed level in Measure Theory books. I really have learnt a lot from this book.

すばらしい本だと思う。3回も改訂されているので、ミスも殆どないし、何よりも本当にていねいな説明で書かれている。419ページと厚いが、その代わりに最後の離散マルチンゲール理論に至るまでくわしく、そして判り易い。ただし、ルベーグ積分についてはしっかりとした知識を持っていないといけないだろう。ルベーグ積分を前提として書かれている日本語の確率論の本、例えば西尾真喜子「確率論」などを読んでから取り組むのも良いだろう。