Probability with Martingales

ISBN-10: 0521406056
ISBN-13: 9780521406055
Edition: 1991
Authors: David Williams
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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  More...

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Book details

List price: $69.99
Copyright year: 1991
Publisher: Cambridge University Press
Publication date: 2/14/1991
Binding: Paperback
Pages: 265
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 0.836
Language: English

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.

A branching-process example
Foundations
Measure spaces
Events
Random variables
Independence
Integration
Expectation
An easy strong law: product measure
Martingale Theory
Conditional expectation
Martingales
The convergence theorem
Martingales bounded in L2
Uniform integrability
UI martingales
Applications
Characteristic Functions
Basic properties of CFs
Weak convergence
The central limit theorem
Appendices
Exercises

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