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A User's Guide to Measure Theoretic Probability

A User's Guide to Measure Theoretic Probability

Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: March 2002
  • availability: Available
  • format: Paperback
  • isbn: 9780521002899

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  • Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.

    • Numerous exercises
    • Contains many comments, explanations and aids to intuition, not just wall-to-wall mathematics
    • Unusual treatment of advanced topics, using streamlined notation and methods accessible to students who have not studied probability at this level before
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    'A really useful book …'. EMS Newsletter

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    Product details

    • Date Published: March 2002
    • format: Paperback
    • isbn: 9780521002899
    • length: 366 pages
    • dimensions: 255 x 181 x 21 mm
    • weight: 0.64kg
    • contains: 200 exercises
    • availability: Available
  • Table of Contents

    1. Motivation
    2. A modicum of measure theory
    3. Densities and derivatives
    4. Product spaces and independence
    5. Conditioning
    6. Martingale et al
    7. Convergence in distribution
    8. Fourier transforms
    9. Brownian motion
    10. Representations and couplings
    11. Exponential tails and the law of the iterated logarithm
    12. Multivariate normal distributions
    Appendix A. Measures and integrals
    Appendix B. Hilbert spaces
    Appendix C. Convexity
    Appendix D. Binomial and normal distributions
    Appendix E. Martingales in continuous time
    Appendix F. Generalized sequences.

  • Author

    David Pollard, Yale University, Connecticut

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