Probability: A Graduate Course A Graduate Course - Gut, Allan; SpringerLink (Online service) (New York, NY : Springer New York : Imprint: Springer, 2013)
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.
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.
Keywords: Mathematics; Distribution (Probability theory).; Statistics; Mathematical statistics; Mathematics; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Statistics, general