A course in probability theory /:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
San Diego :
Academic Press,
©2001.
|
| Ausgabe: | 3rd ed. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1 online resource (xvi, 419 pages) |
| Bibliographie: | Includes bibliographical references (pages 413-414) and index. |
| ISBN: | 9780080522982 008052298X |
Internformat
MARC
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| 245 | 1 | 2 | |a A course in probability theory / |c Kai Lai Chung. |
| 250 | |a 3rd ed. | ||
| 260 | |a San Diego : |b Academic Press, |c ©2001. | ||
| 300 | |a 1 online resource (xvi, 419 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 504 | |a Includes bibliographical references (pages 413-414) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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 Note -- Chapter 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 smartingales -- 9.4 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 -- Last Page | |
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| author | Chung, Kai Lai, 1917-2009 |
| author_GND | http://id.loc.gov/authorities/names/n79026666 |
| author_facet | Chung, Kai Lai, 1917-2009 |
| author_role | |
| author_sort | Chung, Kai Lai, 1917-2009 |
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| 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 Note -- Chapter 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 smartingales -- 9.4 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 -- Last Page |
| ctrlnum | (OCoLC)179869682 |
| dewey-full | 519.2 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3rd ed. |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:10Z |
| institution | BVB |
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| spelling | Chung, Kai Lai, 1917-2009. https://id.oclc.org/worldcat/entity/E39PBJf4bk3x6kxb3GqJXqBgKd http://id.loc.gov/authorities/names/n79026666 A course in probability theory / Kai Lai Chung. 3rd ed. San Diego : Academic Press, ©2001. 1 online resource (xvi, 419 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 413-414) and index. Print version record. 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 Note -- Chapter 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 smartingales -- 9.4 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 -- Last Page Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Probabilités. probability. aat MATHEMATICS Probability & Statistics General. bisacsh Probabilities fast Print version: Chung, Kai Lai, 1917-2009. Course in probability theory. 3rd ed. San Diego : Academic Press, ©2001 0121741516 9780121741518 (DLC) 00106712 (OCoLC)45622341 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=196455 Volltext |
| spellingShingle | Chung, Kai Lai, 1917-2009 A course in probability theory / 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 Note -- Chapter 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 smartingales -- 9.4 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 -- Last Page Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Probabilités. probability. aat MATHEMATICS Probability & Statistics General. bisacsh Probabilities fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85107090 |
| title | A course in probability theory / |
| title_auth | A course in probability theory / |
| title_exact_search | A course in probability theory / |
| title_full | A course in probability theory / Kai Lai Chung. |
| title_fullStr | A course in probability theory / Kai Lai Chung. |
| title_full_unstemmed | A course in probability theory / Kai Lai Chung. |
| title_short | A course in probability theory / |
| title_sort | course in probability theory |
| topic | Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Probabilités. probability. aat MATHEMATICS Probability & Statistics General. bisacsh Probabilities fast |
| topic_facet | Probabilities. Probabilités. probability. MATHEMATICS Probability & Statistics General. Probabilities |
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