A Course in Probability Theory / Edition 3

by Kai Lai Chung

Overview

Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses.

While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.

Product Details

ISBN-13:	9780121741518
Publisher:	Elsevier Science
Publication date:	10/09/2000
Edition description:	REVISED
Pages:	419
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Kai Lai Chung is a Professor Emeritus at Stanford University and has taught probability theory for 30 years.

Table of Contents

Preface to the third edition		ix
Preface to the second edition		xi
Preface to the first edition		xiii
Distribution function
Monotone function		1	(6)
Distribution functions		7	(4)
Absolutely continuous and singular distributions		11	(5)
Measure theory
Classes of sets		16	(5)
Probability measures and their distribution functions		21	(13)
Random variable. Expectation. Independence
General definitions		34	(7)
Properties of mathematical expectation		41	(12)
Independence		53	(15)
Convergence concepts
Various modes of convergence		68	(7)
Almost sure convergence; Borel-Cantelli lemma		75	(9)
Vague convergence		84	(7)
Continuation		91	(8)
Uniform integrability; convergence of moments		99	(7)
Law of large numbers. Random series
Simple limit theorems		106	(6)
Weak law of large numbers		112	(9)
Convergence of series		121	(8)
Strong law of large numbers		129	(9)
Applications		138	(12)
Bibliographical Note		148	(2)
Characteristic function
General properties; convolutions		150	(10)
Uniqueness and inversion		160	(9)
Convergence theorems		169	(6)
Simple applications		175	(12)
Representation theorems		187	(9)
Multidimensional case; Laplace transforms		196	(9)
Bibliographical Note		204	(1)
Central limit theorem and its ramifications
Liapounov's theorem		205	(9)
Lindeberg-Feller theorem		214	(10)
Ramifications of the central limit theorem		224	(11)
Error estimation		235	(7)
Law of the iterated logarithm		242	(8)
Infinite divisibility		250	(13)
Bibliographical Note		261	(2)
Random walk
Zero-or-one laws		263	(7)
Basic notions		270	(8)
Recurrence		278	(10)
Fine structure		288	(10)
Continuation		298	(12)
Bibliographical Note		308	(2)
Conditioning. Markov property. Martingale
Basic properties of conditional expectation		310	(12)
Conditional independence; Markov property		322	(12)
Basic properties of smartingales		334	(12)
Inequalities and convergence		346	(14)
Applications		360	(15)
Bibliographical Note		373	(2)
Supplement: Measure and Integral
Construction of measure		375	(5)
Characterization of extensions		380	(7)
Measures in R		387	(8)
Integral		395	(12)
Applications		407	(6)
General Bibliography		413	(2)
Index		415

Editorial Reviews

A text for a probability course, popular since publication of the first edition in 1968. Coverage includes distribution function, measure theory, random variables and properties of mathematical expectation, convergence concepts, the law of large numbers, and random series. Other topics covered include characteristic function, central limit theorem and its ramifications, random walk, conditioning, Markov property, and properties of super- and submartingales. This third edition contains new material on measure and integral. The author is affiliated with Stanford University. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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