Chung A Course in Probability Theory

2. Auflage 2014
ISBN: 978-0-08-057040-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 365 Seiten, Web PDF

This book contains about 500 exercises consisting mostly of special cases and examples, second thoughts and alternative arguments, natural extensions, and some novel departures. With a few obvious exceptions they are neither profound nor trivial, and hints and comments are appended to many of them. If they tend to be somewhat inbred, at least they are relevant to the text and should help in its digestion. As a bold venture I have marked a few of them with a * to indicate a 'must', although no rigid standard of selection has been used. Some of these are needed in the book, but in any case the reader's study of the text will be more complete after he has tried at least those problems.

Kai Lai Chung is a Professor Emeritus at Stanford University and has taught probability theory for 30 years.

Autoren/Hrsg.

Chung, Kai Lai

Inhaltsverzeichnis

1;Front Cover;1
2;A Course in Probability Theory;3
3;Copyright Page;5
4;Table of Contents;6
5;Preface;8
6;Preface to the first edition;10
7; Chapter 1. Distribution function;16
7.1;1.1 Monotone functions;16
7.2;1.2 Distribution functions;22
7.3;1.3 Absolutely continuous and singular distributions;25
8;Chapter 2. Measure theory;30
8.1;2.1 Classes of sets;30
8.2;2.2 Probability measures and their distribution functions;35
9;Chapter 3. Random variable. Expectation. Independence;47
9.1;3.1 General definitions;47
9.2;3.2 Properties of mathematical expectation;54
9.3;3.3 Independence;64
10;Chapter 4. Convergence concepts;79
10.1;4.1 Various modes of convergence;79
10.2;4.2 Almost sure convergence; Borel-Cantelli lemma;86
10.3;4.3 Vague convergence;94
10.4;4.4 Continuation;101
10.5;4.5 Uniform integrability; convergence of moments;109
11;Chapter 5. Law of large numbers. Random series;116
11.1;5.1 Simple limit theorems;116
11.2;5.2 Weak law of large numbers;122
11.3;5.3 Convergence of series;130
11.4;5.4 Strong law of large numbers;138
11.5;5.5 Applications;146
11.6;Bibliographical Not;156
12;Chapter 6. Characteristic function;157
12.1;6.1 General properties; convolutions;157
12.2;6.2 Uniqueness and inversion;167
12.3;6.3 Convergence theorems;175
12.4;6.4 Simple applications;181
12.5;6.5 Representation theorems;193
12.6;6.6 Multidimensional case; Laplace transforms;202
12.7;Bibliographical Note;210
13;Chapter 7. Central limit theoremand its ramifications;211
13.1;7.1 Liapounov's theorem;211
13.2;7.2 Lindeberg-Feller theorem;220
13.3;7.3 Ramifications of the central limit theorem;229
13.4;7.4 Error estimation;239
13.5;7.5 Law of the iterated logarithm;246
13.6;7.6 Infinite divisibility;253
13.7;Bibliographical Note;264
14;Chapter 8. Random walk;265
14.1;8.1 Zero-or-one laws;265
14.2;8.2 Basic notions;272
14.3;8.3 Recurrence;281
14.4;8.4 Fine structure;290
14.5;8.5 Continuation;300
14.6;Bibliographical Note;308
15;Chapter 9. Conditioning. Markovproperty. Martingale;310
15.1;9.1 Basic properties of conditional expectation;310
15.2;9.2 Conditional independence; Markov property;321
15.3;9.3 Basic properties of smartingales;333
15.4;9.4 Inequalities and convergence;345
15.5;9.5 Applications;358
15.6;Bibliographical Note;371
15.7;General bibliography;373
15.8;Index;376