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Probability: a graduate course/ Allan Gut

By: Material type: TextTextLanguage: English Series: Springer Texts in StatisticsPublication details: New York: Springer, 2013Edition: 2ndDescription: xxv, 600 pages; 24 cmISBN:
  • 9781461447078
Subject(s): DDC classification:
  • 23rd. 519.2 G983
Contents:
Introductory Measure Theory -- Random Variables -- Inequalities -- Characteristic Functions -- Convergence -- The Law of Large Numbers -- The Central Limit Theorem -- The Law of the Iterated Logarithm -- Limit Theorems Extensions and Generalizations -- Martingales
Summary: Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references.
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Includes index and references

Introductory Measure Theory -- Random Variables -- Inequalities -- Characteristic Functions -- Convergence -- The Law of Large Numbers -- The Central Limit Theorem -- The Law of the Iterated Logarithm -- Limit Theorems Extensions and Generalizations -- Martingales

Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references.

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