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Probability
Theory and Examples

5th Edition

$64.00 USD

Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: April 2019
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108584586

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  • This lively introduction to measure-theoretic probability theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. Concentrating on results that are the most useful for applications, this comprehensive treatment is a rigorous graduate text and reference. Operating under the philosophy that the best way to learn probability is to see it in action, the book contains extended examples that apply the theory to concrete applications. This fifth edition contains a new chapter on multidimensional Brownian motion and its relationship to partial differential equations (PDEs), an advanced topic that is finding new applications. Setting the foundation for this expansion, Chapter 7 now features a proof of Itô's formula. Key exercises that previously were simply proofs left to the reader have been directly inserted into the text as lemmas. The new edition re-instates discussion about the central limit theorem for martingales and stationary sequences.

    • Provides 200 examples and 450 problems to equip readers to build practical intuition and understand the motivation for the theory
    • Offers a modern selection of topics, including multidimensional Brownian motion
    • The compact style strikes a balance between completeness and readability, covering a great deal of ground in 400 pages
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    Product details

    • Edition: 5th Edition
    • Date Published: April 2019
    • format: Adobe eBook Reader
    • isbn: 9781108584586
    • contains: 20 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    1. Measure theory
    2. Laws of large numbers
    3. Central limit theorems
    4. Martingales
    5. Markov chains
    6. Ergodic theorems
    7. Brownian motion
    8. Applications to random walk
    9. Multidimensional Brownian motion
    Appendix. Measure theory details.

  • Author

    Rick Durrett, Duke University, North Carolina
    Rick Durrett is a James B. Duke professor in the mathematics department of Duke University, North Carolina. He received his Ph.D. in Operations Research from Stanford University in 1976. After nine years at University of California, Los Angeles and twenty-five at Cornell University, he moved to Duke University in 2010. He is the author of 8 books and more than 220 journal articles on a wide variety of topics, and has supervised more than 45 Ph.D. students. He is a member of National Academy of Science, American Academy of Arts and Sciences, and a fellow of the Institute of Mathematical Statistics, and of the American Mathematical Society.

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