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Probability with Martingales

Probability with Martingales

$46.99 (X)

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  • Author: David Williams, Statistical Laboratory, University of Cambridge
  • Date Published: February 1991
  • availability: In stock
  • format: Paperback
  • isbn: 9780521406055

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About the Authors
  • 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.

    • First text written for students that covers essential ideas
    • Class tested
    • World famous statistician
    • Established author (with Wiley unfortunately)
    • Inimitable style
    • Martingales increasingly important for applications, e.g. to econometrics
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    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

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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: In stock
  • 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
  • Author

    David Williams, Statistical Laboratory, University of Cambridge

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