Probability with Martingales

Probability with Martingales (Cambridge Mathematical Textbooks) 1st Edition
by David Williams(Author)
Publisher: Cambridge University Press; 1st edition (February 22, 1991)
Language: English
Paperback: 251 pages
ISBN-10: 0521406056
ISBN-13: 9780521406055
Book Description
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 Numbers and Three-Series Theorem are proved by martingale techniques. A proof of the Central Limit Theorem is also given. The author's style is entertaining and inimitable with pedagogy to the fore. Exercises play a vital role; there is a full quota of interesting and challenging problems, some with hints.