Probability with Martingales

Probability with Martingales

by David Williams
     
 

View All Available Formats & Editions

ISBN-10: 0521406056

ISBN-13: 9780521406055

Pub. Date: 02/28/1991

Publisher: Cambridge University Press

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

Overview

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.

Product Details

ISBN-13:
9780521406055
Publisher:
Cambridge University Press
Publication date:
02/28/1991
Edition description:
New Edition
Pages:
272
Sales rank:
1,031,168
Product dimensions:
5.98(w) x 8.98(h) x 0.67(d)

Related Subjects

Table of Contents

1. A branching-process example; Part I. Foundations: 2. Measure spaces; 3. Events; 4. Random variables; 5. Independence; 6. Integration; 7. Expectation; 8. An easy strong law: product measure; Part II. Martingale Theory: 9. Conditional expectation; 10. Martingales; 11. The convergence theorem; 12. Martingales bounded in L2; 13. Uniform integrability; 14. UI martingales; 15. Applications; Part III. Characteristic Functions: 16. Basic properties of CFs; 17. Weak convergence; 18. The central limit theorem; Appendices; Exercises.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >