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Course in Probability Theory

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ISBN-10: 0121741516

ISBN-13: 9780121741518

Edition: 2nd 2001 (Revised)

Authors: Kai Lai Chung

List price: $98.95
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This text was first published over 30 years ago and is accessible to many undergraduate programs and as a first-year graduate text. It offers a broad perspective on probability theory with a new appendix on measure theory.
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Book details

List price: $98.95
Edition: 2nd
Copyright year: 2001
Publisher: Elsevier Science & Technology Books
Publication date: 10/9/2000
Binding: Paperback
Pages: 419
Size: 6.00" wide x 8.75" long x 1.00" tall
Weight: 1.298
Language: English

Preface to the third edition
Preface to the second edition
Preface to the first edition
Distribution function
Monotone functions
Distribution functions
Absolutely continuous and singular distributions
Measure theory
Classes of sets
Probability measures and their distribution functions
Random variable. Expectation. Independence
General definitions
Properties of mathematical expectation
Convergence concepts
Various modes of convergence
Almost sure convergence; Borel-Cantelli lemma
Vague convergence
Uniform integrability; convergence of moments
Law of large numbers. Random series
Simple limit theorems
Weak law of large numbers
Convergence of series
Strong law of large numbers
Bibliographical Note
Characteristic function
General properties; convolutions
Uniqueness and inversion
Convergence theorems
Simple applications
Representation theorems
Multidimensional case; Laplace transforms
Bibliographical Note
Central limit theorem and its ramifications
Liapounov's theorem
Lindeberg-Feller theorem
Ramifications of the central limit theorem
Error estimation
Law of the iterated logarithm
Infinite divisibility
Bibliographical Note
Random walk
Zero-or-one laws
Basic notions
Fine structure
Bibliographical Note
Conditioning. Markov property. Martingale
Basic properties of conditional expectation
Conditional independence; Markov property
Basic properties of smartingales
Inequalities and convergence
Bibliographical Note
Supplement: Measure and Integral
Construction of measure
Characterization of extensions
Measures in R
General Bibliography