AuthorGut, Allan. author
TitleProbability: A Graduate Course [electronic resource] : A Graduate Course / by Allan Gut
ImprintNew York, NY : Springer New York : Imprint: Springer, 2013
Edition 2nd ed. 2013
Connect tohttp://dx.doi.org/10.1007/978-1-4614-4708-5
Descript XXV, 600 p. 13 illus. online resource

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


CONTENT

Preface to the First Edition -- Preface to the Second Edition -- Outline of Contents -- Notation and Symbols -- Introductory Measure Theory -- Random Variables -- Inequalities -- Characteristic Functions -- Convergence -- The Law of Large Numbers -- The Central Limit Theorem -- The Law of the Iterated Logarithm -- Limited Theorems -- Martingales -- Some Useful Mathematics -- References -- Index


SUBJECT

  1. Mathematics
  2. Distribution (Probability theory)
  3. Statistics
  4. Mathematical statistics
  5. Mathematics
  6. Probability Theory and Stochastic Processes
  7. Statistical Theory and Methods
  8. Statistics
  9. general