Allan Gut: Probability: A Graduate Course

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Cover: 9781461447078 | Probability: A Graduate Course | Allan Gut | Buch | XXVI | Englisch

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Allan Gut is Professor of Mathematical Statistics in the Department of Mathematics at Uppsala University, Sweden.

Zusammenfassung

Covers probability from a very applied perspective

Many exercises involve mathematical modeling of random phenomena in very practical fields, including insurance/actuarial and the life sciences/biomedicine

Second edition comprehensively updated, including all new exercises

Includes supplementary material: [...]

Inhaltsverzeichnis

¿¿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.