Probability theory independence, interchangeability, martingales
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1988
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer texts in statistics.
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Probability theory |b independence, interchangeability, martingales |c Yuan Shih Chow ; Henry Teicher |
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Datensatz im Suchindex
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| _version_ | 1823051882882400256 |
| adam_text | Titel: Probability theory
Autor: Chow, Yuan Shih
Jahr: 1988
Contents Preface to the Second Edition vii Preface to the First Edition ix List of Abbreviations xvi List of Symbols and Conventions xvii 1 Classes of Sets, Measures, and Probability Spaces 1 1.1 Sets and set operations 1 1.2 Spaces and indicators 4 1.3 Sigma-algebras, measurable spaces, and product spaces 6 1.4 Measurable transformations 12 1.5 Additive set functions, measures, and probability spaces 18 1.6 Induced measures and distribution functions 25 2 Binomial Random Variables 30 2.1 Poisson theorem, interchangeable events, and their limiting probabilities 30 2.2 Bernoulli, Borel theorems 39 2.3 Central limit theorem for binomial random variables, large deviations 45 3 Independence 54 3.1 Independence, random allocation of balls into cells 54 3.2 Borel-Cantelli theorem, characterization of independence, Kolmogorov zero-one law 60 Xlll
Contents 3.3 Convergence in probability, almost certain convergence, and their equivalence for sums of independent random variables 65 3.4 Bernoulli trials 75 4 Integration in a Probability Space 84 4.1 Definition, properties of the integral, monotone convergence theorem 84 4.2 Indefinite integrals, uniform integrability, mean convergence 92 4.3 Jensen, Holder, Schwarz inequalities 103 5 Sums of Independent Random Variables 113 5.1 Three series theorem 113 5.2 Laws of large numbers 124 5.3 Stopping times, copies of stopping times, Wald’s equation 135 5.4 Chung-Fuchs theorem, elementary renewal theorem, optimal stopping 144 6 Measure Extensions, Lebesgue-Stieltjes Measure, Kolmogorov Consistency Theorem 159 6.1 Measure extensions, Lebesgue-Stieltjes measure 159 6.2 Integration in a measure space 165 6.3 Product measure, Fubini’s theorem, n-dimensional Lebesgue-Stieltjes measure 178 6.4 Infinite-dimensional product measure space, Kolmogorov consistency theorem 185 6.5 Absolute continuity of measures, distribution functions; Radon-Nikodym theorem 194 7 Conditional Expectation, Conditional Independence, Introduction to Martingales 202 7.1 Conditional expectations 202 7.2 Conditional probabilities, conditional probability measures 214 7.3 Conditional independence, interchangeable random variables 221 7.4 Introduction to martingales 231 8 Distribution Functions and Characteristic Functions 252 8.1 Convergence of distribution functions, uniform integrability, Helly-Bray theorem 252
Contents XV 8.2 Weak compactness, Frechet-Shohat, Glivenko- Cantelli theorems 263 8.3 Characteristic functions, inversion formula, Levy continuity theorem 268 8.4 The nature of characteristic functions, analytic characteristic functions, Cramer-Levy theorem 276 8.5 Remarks on k-dimensional distribution functions and characteristic functions 290 9 Central Limit Theorems 295 9.1 Independent components 295 9.2 Interchangeable components 309 9.3 The martingale case 318 9.4 Miscellaneous central limit theorems 321 9.5 Central limit theorems for double arrays 327 10 Limit Theorems for Independent Random Variables 336 10.1 Laws of large numbers 336 10.2 Law of the iterated logarithm 350 10.3 Marcinkiewicz-Zygmund inequality, dominated ergodic theorems 366 10.4 Maxima of random walks 373 11 Martingales 386 11.1 Upcrossing inequality and convergence 386 11.2 Martingale extension of Marcinkiewicz- Zygmund inequalities 394 11.3 Convex function inequalities for martingales 403 11.4 Stochastic inequalities 413 12 Infinitely Divisible Laws 424 12.1 Infinitely divisible characteristic functions 424 12.2 Infinitely divisible laws as limits 434 12.3 Stable laws 448 Index 458
|
| any_adam_object | 1 |
| author | Chow, Yuan Shih 1924- Teicher, Henry 1922- |
| author_GND | (DE-588)1031598707 (DE-588)1031598804 |
| author_facet | Chow, Yuan Shih 1924- Teicher, Henry 1922- |
| author_role | aut aut |
| author_sort | Chow, Yuan Shih 1924- |
| author_variant | y s c ys ysc h t ht |
| building | Verbundindex |
| bvnumber | BV002212623 |
| callnumber-first | Q - Science |
| callnumber-label | QA273C573 1988 |
| callnumber-raw | QA273C573 1988 |
| callnumber-search | QA273C573 1988 |
| callnumber-sort | QA 3273 C573 41988 |
| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 600f |
| ctrlnum | (OCoLC)299463178 (DE-599)BVBBV002212623 |
| 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 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2025-02-03T16:44:36Z |
| institution | BVB |
| isbn | 0387966951 3540966951 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001453208 |
| oclc_num | 299463178 |
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| physical | XVIII, 467 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in statistics. |
| spellingShingle | Chow, Yuan Shih 1924- Teicher, Henry 1922- Probability theory independence, interchangeability, martingales Martingales (Mathématiques) Probabilités Probabilités ram martingale inriac théorie probabilité inriac théorème limite inriac Martingal (DE-588)4126466-6 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4126466-6 (DE-588)4064324-4 (DE-588)4079013-7 |
| title | Probability theory independence, interchangeability, martingales |
| title_auth | Probability theory independence, interchangeability, martingales |
| title_exact_search | Probability theory independence, interchangeability, martingales |
| title_full | Probability theory independence, interchangeability, martingales Yuan Shih Chow ; Henry Teicher |
| title_fullStr | Probability theory independence, interchangeability, martingales Yuan Shih Chow ; Henry Teicher |
| title_full_unstemmed | Probability theory independence, interchangeability, martingales Yuan Shih Chow ; Henry Teicher |
| title_short | Probability theory |
| title_sort | probability theory independence interchangeability martingales |
| title_sub | independence, interchangeability, martingales |
| topic | Martingales (Mathématiques) Probabilités Probabilités ram martingale inriac théorie probabilité inriac théorème limite inriac Martingal (DE-588)4126466-6 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Martingales (Mathématiques) Probabilités martingale théorie probabilité théorème limite Martingal Wahrscheinlichkeitsrechnung Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001453208&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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