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  3. A User's Guide to Measure Theoretic Probability
  • Cited by 102
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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2011
      December 2001
      ISBN:
      9780511811555
      9780521802420
      9780521002899
      DOI:
      https://doi.org/10.1017/CBO9780511811555
      Dimensions:
      (253 x 177 mm)
      Weight & Pages:
      0.85kg, 366 Pages
      Dimensions:
      (253 x 177 mm)
      Weight & Pages:
      0.652kg, 366 Pages
      • Subjects:
      Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, General Statistics and Probability, Statistics and Probability
      Series:
      Cambridge Series in Statistical and Probabilistic Mathematics (8)
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    Subjects:
    Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, General Statistics and Probability, Statistics and Probability
    Series:
    Cambridge Series in Statistical and Probabilistic Mathematics (8)
    Information

    Book description

    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.

    Reviews

    'A really useful book …'.

    Source: EMS Newsletter

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