Probability with Martingales

Name: Probability with Martingales
Availability: InStock
ISBN: 9780521406055

ISBN-10: 0521406056

ISBN-13: 9780521406055

Edition: 1991

Authors: David Williams

List price: $54.99

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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 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.

Book details

List price: $54.99
Copyright year: 1991
Publisher: Cambridge University Press
Publication date: 2/14/1991
Binding: Paperback
Pages: 265
Size: 5.98" wide x 8.98" long x 0.67" tall
Weight: 1.056




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