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  3. A Basic Course in Measure and Probability
  • Cited by 3
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    • Publisher:
      Cambridge University Press
      Publication date:
      June 2014
      January 2014
      ISBN:
      9781139103947
      9781107020405
      9781107652521
      DOI:
      https://doi.org/10.1017/CBO9781139103947
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.68kg, 376 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.6kg, 374 Pages
      • Subjects:
      Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
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    • Selected: Digital
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    Subjects:
    Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
    Information

    Book description

    Originating from the authors' own graduate course at the University of North Carolina, this material has been thoroughly tried and tested over many years, making the book perfect for a two-term course or for self-study. It provides a concise introduction that covers all of the measure theory and probability most useful for statisticians, including Lebesgue integration, limit theorems in probability, martingales, and some theory of stochastic processes. Readers can test their understanding of the material through the 300 exercises provided. The book is especially useful for graduate students in statistics and related fields of application (biostatistics, econometrics, finance, meteorology, machine learning, and so on) who want to shore up their mathematical foundation. The authors establish common ground for students of varied interests which will serve as a firm 'take-off point' for them as they specialize in areas that exploit mathematical machinery.

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    Contents

    Contents
    References
    References
    Billingsley, P.Convergence of Probability Measures, 2nd edn, Wiley – Interscience, 1999.
    Chung, K.L.A Course in Probability Theory, 3rd edn, Academic Press, 2001.
    Cramér, H., Leadbetter, M.R.Stationary and Related Stochastic Processes, Probability and Mathematical Statistics Series, Wiley, 1967. Reprinted by Dover Publications Inc., 2004.
    Feller, W.An Introduction to Probability Theory and Its Applications, vol. 1, John Wiley & Sons, 1950.
    Halmos, P.R.Measure Theory, Springer-Verlag, 1974.
    Kallenberg, O.Random Measures, 4th edn, Academic Press, 1986.
    Kallenberg, O.Foundations of Modern Probability Theory, 2nd edn, Springer Series in Statistics, Springer-Verlag, 2002.
    Loève, M.Probability Theory I, II, 4th edn, Graduate Texts in Mathematics, vol. 45, Springer-Verlag, 1977.
    Resnick, S.I.Extreme Values, Regular Variation, and Point Processes, 2nd edn, Springer-Verlag, 2008.

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