9780121741518

A Course in Probability Theory, Revised Edition

by
  • ISBN13:

    9780121741518

  • ISBN10:

    0121741516

  • Edition: 2nd
  • Format: Paperback
  • Copyright: 2000-10-09
  • Publisher: Elsevier Science
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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

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