High Dimensional Probability:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1998
|
| Schriftenreihe: | Progress in Probability
43 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings |
| Beschreibung: | 1 Online-Ressource (VIII, 335 p) |
| ISBN: | 9783034888295 9783034897907 |
| DOI: | 10.1007/978-3-0348-8829-5 |
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Datensatz im Suchindex
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| author | Eberlein, Ernst |
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| 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 | 10.1007/978-3-0348-8829-5 |
| format | Electronic eBook |
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| spelling | Eberlein, Ernst Verfasser aut High Dimensional Probability edited by Ernst Eberlein, Marjorie Hahn, Michel Talagrand Basel Birkhäuser Basel 1998 1 Online-Ressource (VIII, 335 p) txt rdacontent c rdamedia cr rdacarrier Progress in Probability 43 What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Topologischer Vektorraum (DE-588)4122383-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift gnd-content Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Topologischer Vektorraum (DE-588)4122383-4 s 2\p DE-604 Hahn, Marjorie Sonstige oth Talagrand, Michel Sonstige oth https://doi.org/10.1007/978-3-0348-8829-5 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 |
| spellingShingle | Eberlein, Ernst High Dimensional Probability Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Topologischer Vektorraum (DE-588)4122383-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4122383-4 (DE-588)4079013-7 (DE-588)1071861417 |
| title | High Dimensional Probability |
| title_auth | High Dimensional Probability |
| title_exact_search | High Dimensional Probability |
| title_full | High Dimensional Probability edited by Ernst Eberlein, Marjorie Hahn, Michel Talagrand |
| title_fullStr | High Dimensional Probability edited by Ernst Eberlein, Marjorie Hahn, Michel Talagrand |
| title_full_unstemmed | High Dimensional Probability edited by Ernst Eberlein, Marjorie Hahn, Michel Talagrand |
| title_short | High Dimensional Probability |
| title_sort | high dimensional probability |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Topologischer Vektorraum (DE-588)4122383-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Topologischer Vektorraum Wahrscheinlichkeitstheorie Konferenzschrift |
| url | https://doi.org/10.1007/978-3-0348-8829-5 |
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