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Available5.0
36 reviews
ISBN 10: 2012941281
ISBN 13: 9781461447078
Author: Allan Gut
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.
1. Introductory Measure Theory
2. Random Variables
3. Inequalities
4. Characteristic Functions
5. Convergence
6. The Law of Large Numbers
7. The Central Limit Theorem
8. The Law of the Iterated Logarithm
9. Limit Theorems: Extensions and Generalizations
10. Martingales
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Tags: Allan Gut, Probability, Graduate
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