Probability: A Graduate Course

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Springer Science & Business Media, Oct 17, 2012 - Mathematics - 602 pages

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.

 

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Contents

A GraduateCourse 1 Introductory Measure Theory
1
A GraduateCourse 2 Random Variables
25
A GraduateCourse 3 Inequalities
118
A GraduateCourse 4 Characteristic Functions
157
A GraduateCourse 5 Convergence
201
A GraduateCourse 6 The Law of Large Numbers
264
A GraduateCourse 7 The Central Limit Theorem
329
A GraduateCourse 8 The Law of the Iterated Logarithm
383
A GraduateCourse 9 Limit Theorems Extensions and Generalizations
423
A GraduateCourse 10 Martingales
467
A GraduateCourse AppendixSome Useful Mathematics
555
A GraduateCourse References
577
A GraduateCourse Index
587
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About the author (2012)

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

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