Probability: A Graduate Course
Subtitle: A Graduate Course
By: by Allan Gut
Contributors: SpringerLink (Online service)
Edition: 2nd ed. 2013.
Series: Springer Texts in Statistics -- 75
Publisher: Springer New York; Imprint: Springer
Published: 2013
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 600
ISBN-13: 9781461447085
Subjects: Probability Theory and Stochastic Processes; Statistics; Statistics, general; Mathematics; Distribution (Probability theory); Mathematical statistics; Statistical Theory and Methods
Description: 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 explanations of the three main subjects in probability: 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.
Table of contents: title: ​​Preface to the First Edition; title: Preface to the Second Edition; title: Outline of Contents; title: Notation and Symbols; title: Introductory Measure Theory; title: Random Variables; title: Inequalities; title: Characteristic Functions; title: Convergence; title: The Law of Large Numbers; title: The Central Limit Theorem; title: The Law of the Iterated Logarithm; title: Limited Theorems; title: Martingales; title: Some Useful Mathematics; title: References; title: Index.<br>.