Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1992
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Schriftenreihe: | Progress in Probability
30 |
Schlagworte: | |
Online-Zugang: | Volltext |
Beschreibung: | Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly |
Beschreibung: | 1 Online-Ressource (XI, 512 p) |
ISBN: | 9781461203674 9781461267287 |
DOI: | 10.1007/978-1-4612-0367-4 |
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490 | 0 | |a Progress in Probability |v 30 | |
500 | |a Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly | ||
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Datensatz im Suchindex
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any_adam_object | |
author | Dudley, Richard M. |
author_facet | Dudley, Richard M. |
author_role | aut |
author_sort | Dudley, Richard M. |
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building | Verbundindex |
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dewey-raw | 519.2 |
dewey-search | 519.2 |
dewey-sort | 3519.2 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
doi_str_mv | 10.1007/978-1-4612-0367-4 |
format | Electronic eBook |
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genre_facet | Konferenzschrift 1991 Brunswick Me. |
id | DE-604.BV042419514 |
illustrated | Not Illustrated |
indexdate | 2024-07-10T01:21:05Z |
institution | BVB |
isbn | 9781461203674 9781461267287 |
language | English |
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series2 | Progress in Probability |
spelling | Dudley, Richard M. Verfasser aut Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference edited by Richard M. Dudley, Marjorie G. Hahn, James Kuelbs Boston, MA Birkhäuser Boston 1992 1 Online-Ressource (XI, 512 p) txt rdacontent c rdamedia cr rdacarrier Progress in Probability 30 Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly Mathematics Functional analysis Distribution (Probability theory) Topology Probability Theory and Stochastic Processes Functional Analysis Mathematik Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1991 Brunswick Me. gnd-content Wahrscheinlichkeit (DE-588)4137007-7 s Banach-Raum (DE-588)4004402-6 s 2\p DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 3\p DE-604 Hahn, Marjorie G. Sonstige oth Kuelbs, James Sonstige oth https://doi.org/10.1007/978-1-4612-0367-4 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 | Dudley, Richard M. Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference Mathematics Functional analysis Distribution (Probability theory) Topology Probability Theory and Stochastic Processes Functional Analysis Mathematik Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Banach-Raum (DE-588)4004402-6 gnd |
subject_GND | (DE-588)4137007-7 (DE-588)4079013-7 (DE-588)4004402-6 (DE-588)1071861417 |
title | Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference |
title_auth | Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference |
title_exact_search | Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference |
title_full | Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference edited by Richard M. Dudley, Marjorie G. Hahn, James Kuelbs |
title_fullStr | Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference edited by Richard M. Dudley, Marjorie G. Hahn, James Kuelbs |
title_full_unstemmed | Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference edited by Richard M. Dudley, Marjorie G. Hahn, James Kuelbs |
title_short | Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference |
title_sort | probability in banach spaces 8 proceedings of the eighth international conference |
topic | Mathematics Functional analysis Distribution (Probability theory) Topology Probability Theory and Stochastic Processes Functional Analysis Mathematik Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Banach-Raum (DE-588)4004402-6 gnd |
topic_facet | Mathematics Functional analysis Distribution (Probability theory) Topology Probability Theory and Stochastic Processes Functional Analysis Mathematik Wahrscheinlichkeit Wahrscheinlichkeitstheorie Banach-Raum Konferenzschrift 1991 Brunswick Me. |
url | https://doi.org/10.1007/978-1-4612-0367-4 |
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