Probability Theory: Independence Interchangeability Martingales
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1978
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the subject, generally attributed to investigations by the renowned french mathematician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933). An axiomatic mold and measure-theoretic framework for probability theory was furnished by Kolmogorov. In this so-called objective or measure-theoretic approach, definitions and axioms are so chosen that the empirical realization of an event is the outcome of a not completely determined physical experiment -an experiment which is at least conceptually capable of indefinite repetition (this notion is due to von Mises). The concrete or intuitive counterpart of the probability of an event is a long run or limiting frequency of the corresponding outcome |
| Beschreibung: | 1 Online-Ressource (XV, 455p) |
| ISBN: | 9781468400625 9781468400649 |
| DOI: | 10.1007/978-1-4684-0062-5 |
Internformat
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| 500 | |a Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the subject, generally attributed to investigations by the renowned french mathematician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933). An axiomatic mold and measure-theoretic framework for probability theory was furnished by Kolmogorov. In this so-called objective or measure-theoretic approach, definitions and axioms are so chosen that the empirical realization of an event is the outcome of a not completely determined physical experiment -an experiment which is at least conceptually capable of indefinite repetition (this notion is due to von Mises). The concrete or intuitive counterpart of the probability of an event is a long run or limiting frequency of the corresponding outcome | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Wahrscheinlichkeitsrechnung |0 (DE-588)4064324-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Martingal |0 (DE-588)4126466-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804153093555748864 |
|---|---|
| any_adam_object | |
| author | Chow, Yuan Shih 1924- |
| author_GND | (DE-588)1031598707 (DE-588)1031598804 |
| author_facet | Chow, Yuan Shih 1924- |
| author_role | aut |
| author_sort | Chow, Yuan Shih 1924- |
| author_variant | y s c ys ysc |
| building | Verbundindex |
| bvnumber | BV042420994 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863883391 (DE-599)BVBBV042420994 |
| 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 |
| doi_str_mv | 10.1007/978-1-4684-0062-5 |
| format | Electronic eBook |
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| id | DE-604.BV042420994 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468400625 9781468400649 |
| language | English |
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| spelling | Chow, Yuan Shih 1924- Verfasser (DE-588)1031598707 aut Probability Theory Independence Interchangeability Martingales by Yuan Shih Chow, Henry Teicher New York, NY Springer US 1978 1 Online-Ressource (XV, 455p) txt rdacontent c rdamedia cr rdacarrier Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the subject, generally attributed to investigations by the renowned french mathematician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933). An axiomatic mold and measure-theoretic framework for probability theory was furnished by Kolmogorov. In this so-called objective or measure-theoretic approach, definitions and axioms are so chosen that the empirical realization of an event is the outcome of a not completely determined physical experiment -an experiment which is at least conceptually capable of indefinite repetition (this notion is due to von Mises). The concrete or intuitive counterpart of the probability of an event is a long run or limiting frequency of the corresponding outcome Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 1\p DE-604 Martingal (DE-588)4126466-6 s 2\p DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 3\p DE-604 Teicher, Henry 1922- Sonstige (DE-588)1031598804 oth https://doi.org/10.1007/978-1-4684-0062-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chow, Yuan Shih 1924- Probability Theory Independence Interchangeability Martingales Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Martingal (DE-588)4126466-6 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4126466-6 (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 by Yuan Shih Chow, Henry Teicher |
| title_fullStr | Probability Theory Independence Interchangeability Martingales by Yuan Shih Chow, Henry Teicher |
| title_full_unstemmed | Probability Theory Independence Interchangeability Martingales by Yuan Shih Chow, Henry Teicher |
| title_short | Probability Theory |
| title_sort | probability theory independence interchangeability martingales |
| title_sub | Independence Interchangeability Martingales |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Martingal (DE-588)4126466-6 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Wahrscheinlichkeitsrechnung Martingal Wahrscheinlichkeitstheorie |
| url | https://doi.org/10.1007/978-1-4684-0062-5 |
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