Probability with Martingales
$54.99 (X)
- Author: David Williams, Statistical Laboratory, University of Cambridge
- Date Published: February 1991
- availability: Available
- format: Paperback
- isbn: 9780521406055
$
54.99
(X)
Paperback
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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.
Read more- A modern, lively and rigorous account of probability theory using discrete-time martingales as the main theme
- The treatment is selective, not encyclopaedic, and presents the essentials in a class-tested manner suitable for students
- Interesting and challenging exercises consolidate what has already been learnt, and provide motivation to investigate the subject further
Reviews & endorsements
"Williams, who writes as though he were reading the reader's mind, does a brilliant job of leaving it all in. And well that he does, since the bridge from basic probability theory to measure theoretic probability can be difficult crossing. Indeed, so lively is the development from scratch of the needed measure theory, that students of real analysis, even those with no special interest in probability, should take note." D.V. Feldman, Choice
See more reviews"...a nice textbook on measure-theoretic probability theory." Jia Gan Wang, Mathematical Reviews
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×Product details
- Date Published: February 1991
- format: Paperback
- isbn: 9780521406055
- length: 265 pages
- dimensions: 228 x 152 x 17 mm
- weight: 0.412kg
- contains: 3 b/w illus.
- availability: Available
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.Instructors have used or reviewed this title for the following courses
- Foundations of Probability and Statistics
- Measure Theory for Probability
- Probability and Stats I
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