A course in probability theory / Kai Lai Chung.

Format:

Book

Author/Creator:

Chung, Kai Lai, 1917-2009.

Language:

English

Subjects (All):

Probabilities.

Physical Description:

1 online resource (439 p.)

Edition:

3rd ed.

Place of Publication:

San Diego : Academic Press, c2001.

Language Note:

English

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.

Contents:

Cover; Title Page; Copyright Page; Contents; Preface to the third edition; Preface to the second edition; Preface to the first edition; Chapter 1. Distribution function; 1.1 Monotone functions; 1.2 Distribution functions; 1.3 Absolutely continuous and singular distributions; Chapter 2. Measure theory; 2.1 Classes of sets; 2.2 Probability measures and their distribution functions; Chapter 3. Random variable. Expectation. Independence; 3.1 General definitions; 3.2 Properties of mathematical expectation; 3.3 Independence; Chapter 4. Convergence concepts; 4.1 Various modes of convergence

4.2 Almost sure convergence Borel-Cantelli lemma; 4.3 Vague convergence; 4.4 Continuation; 4.5 Uniform integrability; convergence of moments; Chapter 5. Law of large numbers. Random series; 5.1 Simple limit theorems; 5.2 Weak law of large numbers; 5.3 Convergence of series; 5.4 Strong law of large numbers; 5.5 Applications; Bibliographical Note; Chapter 6. Characteristic function; 6.1 General properties; convolutions; 6.2 Uniqueness and inversion; 6.3 Convergence theorems; 6.4 Simple applications; 6.5 Representation theorems; 6.6 Multidimensional case; Laplace transforms

Bibliographical NoteChapter 7. Central limit theorem and its ramifications; 7.1 Liapounov's theorem; 7.2 Lindeberg-Feller theorem; 7.3 Ramifications of the central limit theorem; 7.4 Error estimation; 7.5 Law of the iterated logarithm; 7.6 Infinite divisibility; Bibliographical Note; Chapter 8. Random walk; 8.1 Zero-or-one laws; 8.2 Basic notions; 8.3 Recurrence; 8.4 Fine structure; 8.5 Continuation; Bibliographical Note; Chapter 9. Conditioning. Markov property. Martingale; 9.1 Basic properties of conditional expectation; 9.2 Conditional independence; Markov property

9.3 Basic properties of smartingales9.4 Inequalities and convergence; 9.5 Applications; Bibliographical Note; Supplement: Measure and Integral; 1 Construction of measure; 2 Characterization of extensions; 3 Measures in R; 4 Integral; 5 Applications; General Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [413]-414) and index.

ISBN:

1-281-02082-6

9786611020828

0-08-052298-X

OCLC:

437182436