Probability: A Graduate Course [electronic resource] : A Graduate Course / by Allan Gut.
By: Gut, Allan [author.].
Contributor(s): SpringerLink (Online service).
Material type: BookSeries: Springer Texts in Statistics: 75Publisher: New York, NY : Springer New York : Imprint: Springer, 2013Edition: 2nd ed. 2013.Description: XXV, 600 p. 13 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781461447085.Subject(s): Mathematics | Distribution (Probability theory) | Statistics | Mathematical statistics | Mathematics | Probability Theory and Stochastic Processes | Statistical Theory and Methods | Statistics, generalDDC classification: 519.2 Online resources: Click here to access onlinePreface 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.
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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