Probability with Martingales
Probability with Martingales
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$54.99
USDThis 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 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
"...a nice textbook on measure-theoretic probability theory." Jia Gan Wang, Mathematical Reviews
Product details
February 1991Paperback
9780521406055
265 pages
228 × 152 × 17 mm
0.412kg
3 b/w illus.
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.
