Probability: A Graduate Course

2. Auflage 2013
ISBN: 978-1-4614-4707-8
Verlag: Springer

Buch, Englisch, 602 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 10579 g

Reihe: Springer Texts in Statistics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Gut, Allan

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

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.

Über Autor(innen)

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