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Probability with Martingales
This is a masterly introduction to the modern and rigorous theory of probability. The author adopts the martingale theory as his main theme and moves at a lively pace through the subject's rigorous foundations. Measure theory is introduced and then immediately exploited by being applied to real probability theory. Classical results, such as Kolmogorov's Strong Law of Large...more
Paperback, 272 pages
Published
February 14th 1991
by Cambridge University Press
(first published 1991)
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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 bo...more
One more thing: This bo...more
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 Le...more
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 Le...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.
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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, Cambridg...more
More about David Williams...
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, Cambridg...more
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