Vladas Pipiras Ross LeadbetterCambridge University Press, 1/30/2014EAN 9781107020405, ISBN10: 1107020409Hardcover, 376 pages, 23.1 x 15.5 x 2.3 cmLanguage: EnglishOriginating 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.PrefaceAcknowledgements1. Point sets and certain classes of sets2. Measuresgeneral properties and extension3. Measurable functions and transformations4. The integral5. Absolute continuity and related topics6. Convergence of measurable functions, Lp-spaces7. Product spaces8. Integrating complex functions, Fourier theory and related topics9. Foundations of probability10. Independence11. Convergence and related topics12. Characteristic functions and central limit theorems13. Conditioning14. Martingales15. Basic structure of stochastic processesReferencesIndex.
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