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Probability with Martingales

4.05 of 5 stars 4.05  ·  rating details  ·  19 ratings  ·  7 reviews
The author adopts the martingale theory as his main theme in this introduction to the modern theory of probability, which is, perhaps, at a practical level, one of the most useful mathematical theories ever devised.
Paperback, 265 pages
Published February 14th 1991 by Cambridge University Press (first published 1991)
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There is a large gap between classical and modern (measure theoretic) probability theory in that the later seems so much harder. However, without measure theory probability theory lacks a solid theoritical basis and leads to unsurmantouble problems in tryingto define stochastic processes.
I found this to be the best instructional book for those who want to transition from classical to the measure theoretic probability. I am not sure it is the best introductory book for measure theory and Lebesgue
Jun 21, 2011 Joecolelife rated it 5 of 5 stars  ·  review of another edition
Recommended to Joecolelife by:
A Pedagogical Masterpiece
I used this book for self-study after struggling with Billingsley and Chung for months. Williams has a deep love for probability and it comes out rather beautifully in his writing. He gives the various topics just enough attention to maintain the brisk tempo necessary for a first course in measure theoretic probability and his proofs and exposition are on average much clearer than the aforementioned authors'. He has a knack of anticipating the average readers' stumbling
Imagine watching the movie Pulp Fiction for the first time but without any sound. By the end of the movie, you might think you know what went on and you might even be right; but you would likely be wrong in all the details. Reading this book to learn measure theory or probability or martingales is just like watching Pulp Fiction without sound. If you know the details and loved it, you've probably seen the movie already with sound. If you didn't see it already with sound, you don't really know th ...more
one of my favorite math texts, but it's definitely that. not a lot of "practical" examples - if by practical we mean computational - but written in an almost endearing manner totally uncustomary for a math text. not a reference, but excellent presentation for learning.
Fausto Saleri
Inefficient, almost useless for any student. Notations are confuse, theorems are basically left to the reader; the choice behind the appendix is simply wrong, because you need to read it to go through the chapter, why separate things that have not to be separated?
It dares even to laugh at you with ridicolous spoilers, exactly like you would like to drop the read anytime. I never got to see something so childish and unprofessional in a math textbook.
Jun 21, 2011 Joecolelife rated it 5 of 5 stars
Recommended to Joecolelife by:
As the previous reviewers mentioned, this book is a concise and clear introduction to measure based probability. In contrast to some other reviewers, I like it a lot. The proofs ARE clear, the appendices ARE well placed and the order of presentation MAKES a lot of sense. One caveat is in order: since this book is EXTREMELY concise, one may have to think about the proofs and definitions for a while to digest it. The author does not chew up the material for you.

One more thing: This book is not ju
Simple and concise. Essential reading for anyone interested in measure-theoretic probability.
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David Williams is a Welsh mathematician who works in probability theory. He was educated at Gowerton Grammar School, winning a mathematics scholarship to Jesus College, Oxford, and went on to obtain a DPhil. He held posts at Stanford (1962–63), Durham, Cambridge (1966–69)
More about David Williams...
Weighing the Odds: A Course in Probability and Statistics

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