Skip to content
Register Sign in Wishlist
Probability with Martingales

Probability with Martingales

$48.99 (X)

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

$ 48.99 (X)

Add to cart Add to wishlist

Other available formats:

Request examination copy

Instructors may request a copy of this title for examination

Product filter button
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.

    • 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
    Read more

    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

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    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

  • 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

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.