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Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference - Couverture souple
Synopsis
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 Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces.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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- ÉditeurBirkhäuser
- Date d'édition2012
- ISBN 10 1461267285
- ISBN 13 9781461267287
- ReliureBroché
- Langueanglais
- Nombre de pages528
- ÉditeurDudley R.M., Hahn M.G., Kuelbs J.
- Coordonnées du fabricantnon disponible
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Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference
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Birkhäuser Boston, 2012
ISBN 10 : 1461267285
ISBN 13 : 9781461267287
Neuf
Couverture souple
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Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference
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ISBN 10 : 1461267285
ISBN 13 : 9781461267287
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Taschenbuch
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 528 pp. Englisch. N° de réf. du vendeur 9781461267287
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Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference (Progress in Probability)
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Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference
Edité par
Birkhäuser Boston, Birkhäuser Boston Okt 2012, 2012
ISBN 10 : 1461267285
ISBN 13 : 9781461267287
Neuf
Taschenbuch
Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne
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Taschenbuch. Etat : Neu. Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 528 pp. Englisch. N° de réf. du vendeur 9781461267287
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Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference
Edité par
Birkhäuser Boston, Birkhäuser Boston, 2012
ISBN 10 : 1461267285
ISBN 13 : 9781461267287
Neuf
Taschenbuch
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9781461267287
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Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference (Progress in Probability)
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Probability in Banach Spaces, 8
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Probability in Banach Spaces, 8
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Probability in Banach Spaces, 8
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Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference (Progress in Probability, 30)
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Birkhäuser, 2012
ISBN 10 : 1461267285
ISBN 13 : 9781461267287
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