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A course in probability theory

Author: Kai Lai Chung
Publisher: San Diego : Academic Press, ©2001.
Edition/Format:   Print book : English : 3rd edView all editions and formats
Database:WorldCat
Summary:

This book is designed for undergraduate programs and students and can also be used as a first-year graduate text in probability. It offers a broad perspective, building on the synopsis of measure and  Read more...

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Genre/Form: Einführung
Document Type: Book
All Authors / Contributors: Kai Lai Chung
ISBN: 0121741516 9780121741518
OCLC Number: 45622341
Notes: "Transferred to Digital Printing 2011"--Title page verso.
Description: xvi, 419 pages ; 23 cm
Contents: 1 Distribution function --
1.1 Monotone functions 1 --
1.2 Distribution functions 7 --
1.3 Absolutely continuous and singular distributions 11 --
2 Measure theory --
2.1 Classes of sets 16 --
2.2 Probability measures and their distribution functions 21 --
3 Random variable: Expectation: Independence --
3.1 General definitions 34 --
3.2 Properties of mathematical expectation 41 --
3.3 Independence 53 --
4 Convergence concepts --
4.1 Various modes of convergence 68 --
4.2 Almost sure convergence; Borel-Cantelli lemma 75 --
4.3 Vague convergence 84 --
4.4 Continuation 91 --
4.5 Uniform integrability; convergence of moments 99 --
5 Law of large numbers: Random series --
5.1 Simple limit theorems 106 --
5.2 Weak law of large numbers 112 --
5.3 Convergence of series 121 --
5.4 Strong law of large numbers 129 --
5.5 Applications 138 --
6 Characteristic function --
6.1 General properties; convolutions 150 --
6.2 Uniqueness and inversion 160 --
6.3 Convergence theorems 169 --
6.4 Simple applications 175 --
6.5 Representation theorems 187 --
6.6 Multidimensional case; Laplace transforms 196 --
7 Central limit theorem and its ramifications --
7.1 Liapounov's theorem 205 --
7.2 Lindeberg-Feller theorem 214 --
7.3 Ramifications of the central limit theorem 224 --
7.4 Error estimation 235 --
7.5 Law of the iterated logarithm 242 --
7.6 Infinite divisibility 250 --
8 Random walk --
8.1 Zero-or-one laws 263 --
8.2 Basic notions 270 --
8.3 Recurrence 278 --
8.4 Fine structure 288 --
8.5 Continuation 298 --
9 Conditioning: Markov property: Martingale --
9.1 Basic properties of conditional expectation 310 --
9.2 Conditional independence; Markov property 322 --
9.3 Basic properties of smartingales 334 --
9.4 Inequalities and convergence 346 --
9.5 Applications 360 --
Supplement: Measure and Integral --
1 Construction of measure 375 --
2 Characterization of extensions 380 --
3 Measures in R 387 --
4 Integral 395 --
5 Applications 407.
Responsibility: Kai Lai Chung.
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