Probability: A Graduate Course
Gut, Allan.
Probability: A Graduate Course A Graduate Course / [electronic resource] : by Allan Gut. - 2nd ed. 2013. - XXVI, 602 p. online resource. - Springer Texts in Statistics, 75 1431-875X ; . - Springer Texts in Statistics, 75 .
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.
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.
9781461447085
10.1007/978-1-4614-4708-5 doi
Mathematics.
Probabilities.
Statistics.
Mathematics.
Probability Theory and Stochastic Processes.
Statistical Theory and Methods.
Statistics, general.
QA273.A1-274.9 QA274-274.9
519.2
Probability: A Graduate Course A Graduate Course / [electronic resource] : by Allan Gut. - 2nd ed. 2013. - XXVI, 602 p. online resource. - Springer Texts in Statistics, 75 1431-875X ; . - Springer Texts in Statistics, 75 .
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.
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.
9781461447085
10.1007/978-1-4614-4708-5 doi
Mathematics.
Probabilities.
Statistics.
Mathematics.
Probability Theory and Stochastic Processes.
Statistical Theory and Methods.
Statistics, general.
QA273.A1-274.9 QA274-274.9
519.2