A course in probability theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York and London
Academic Press
1974
|
| Ausgabe: | second edition ; Standford University |
| Schriftenreihe: | Probability and mathematical statistics
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 365 Seiten |
| ISBN: | 012174650X |
Internformat
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Datensatz im Suchindex
| _version_ | 1804117009097555968 |
|---|---|
| adam_text | Titel: A course in probability theory
Autor: Chung, Kai Lai
Jahr: 1974
Preface vii
Preface to the first edition ix
1 | Distribution function
1.1 Monotone functions 1
1.2 Distribution functions 7
1.3 Absolutely continuous and singular distributions 10
2 | Measure theory
2.1 Classes of sets 15
2.2 Probability measures and their distribution functions
3 | Random variable. Expectation. Independence
3.1 General definitions 32
3.2 Properties of mathematical expectation 39
3.3 Independence 49
4 | Convergence concepts
4.1 Various modes of convergence 64
4.2 Almost sure convergence; Borel-Cantelli lemma 71
4.3 Vague convergence 79
CONTENTS
4.4 Continuation 86
4.5 Uniform integrability; convergence of moments 94
5 | Law of large numbers. Random series
5.1 Simple limit theorems 101
5.2 Weak law of large numbers 107
5.3 Convergence of series 115
5.4 Strong law of large numbers 123
5.5 Applications 131
Bibliographical note 141
6 | Characteristic function
6.1 General properties; convolutions 142
6.2 Uniqueness and inversion 152
6.3 Convergence theorems 160
6.4 Simple applications 166
6.5 Representation theorems 178
6.6 Multidimensional case; Laplace transforms 187
Bibliographical note 195
7 | Central limit theorem and its ramifications
7.1 Liapounov s theorem 196
7.2 Lindeberg-Feller theorem 205
7.3 Ramifications of the central limit theorem 214
7.4 Error estimation 224
7.5 Law of the iterated logarithm 231
7.6 Infinite divisibility 238
Bibliographical note 249
8 | Random walk
8.1 Zero-or-one laws 250
8.2 Basic notions 257
8.3 Recurrence 266
8.4 Fine structure 275
8.5 Continuation 285
Bibliographical note 293
9 | Conditioning. Markov property. Martingale
9.1 Basic properties of conditional expectation 295
9.2 Conditional independence; Markov property 306
9.3 Basic properties of smartingales 318
9.4 Inequalities and convergence 330
9.5 Applications 343
Bibliographical note 356
General Bibliography 358
Index 361
|
| any_adam_object | 1 |
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| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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 Wirtschaftswissenschaften |
| edition | second edition ; Standford University |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV002624975 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:47:35Z |
| institution | BVB |
| isbn | 012174650X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001686872 |
| oclc_num | 793410 |
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| physical | xii, 365 Seiten |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Academic Press |
| record_format | marc |
| series | Probability and mathematical statistics |
| series2 | Probability and mathematical statistics |
| spelling | Chung, Kai Lai 1917-2009 (DE-588)136125484 aut A course in probability theory Kai Lai Chung second edition ; Standford University New York and London Academic Press 1974 xii, 365 Seiten txt rdacontent n rdamedia nc rdacarrier Probability and mathematical statistics 21 Probabilidade (Estatistica) larpcal Probabilités Waarschijnlijkheidstheorie gtt Operations Research Probabilities Probability Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Probability and mathematical statistics 21 (DE-604)BV000892568 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001686872&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chung, Kai Lai 1917-2009 A course in probability theory Probability and mathematical statistics Probabilidade (Estatistica) larpcal Probabilités Waarschijnlijkheidstheorie gtt Operations Research Probabilities Probability Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4064324-4 (DE-588)4151278-9 |
| 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 | a course in probability theory |
| topic | Probabilidade (Estatistica) larpcal Probabilités Waarschijnlijkheidstheorie gtt Operations Research Probabilities Probability Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Probabilidade (Estatistica) Probabilités Waarschijnlijkheidstheorie Operations Research Probabilities Probability Wahrscheinlichkeitstheorie Wahrscheinlichkeitsrechnung Einführung |
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