A Course in Probability Theory, Revised Edition

by Chung

• ISBN13: 9780121741518
• ISBN10: 0121741516
• Edition: 2nd
• Format: Paperback
• Copyright: 2000-10-09
• Publisher: Elsevier Science

Summary

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.

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