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High Dimensional Probability ISBN 13 : 9783764358679

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9783764358679: High Dimensional Probability

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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.

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9783034897907: High Dimensional Probability

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ISBN 10 :  3034897901 ISBN 13 :  9783034897907
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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. N° de réf. du vendeur 5279212

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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9783764358679

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Buch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 348 pp. Englisch. N° de réf. du vendeur 9783764358679

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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 335 pp. Englisch. N° de réf. du vendeur 9783764358679

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Hardcover. Etat : new. Hardcover. What is high dimensional probability? Under this broad term this text presents a collection of topics associated by the fact that n plays a key role in each whether the idea of high dimension n is expressed in the problem or in the methods by which it is approached. For example, the study of probability in Banach spaces gave impetus to a number of methods whose importance has gone far beyond the original goal of extending limit laws to the vector valued case. Familiar applications are in the areas of empirical processes, the use of majorizing measures to study regularly of stochastic processes, and the theory of concentration of measure. Many of the ideas, results and directions of this evolving field were explored on a broad front at the Conference on High Dimensional Probability held at Obwerwolfach in August 1996. This collection of referred papers explores many of the ideas, results and directions in the new field of high dimensional probability, which comprises topics where high dimension plays a key role either in the problems or the methods of approaching them. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9783764358679

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Ernst Eberlein
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Hardcover. Etat : new. Hardcover. What is high dimensional probability? Under this broad term this text presents a collection of topics associated by the fact that n plays a key role in each whether the idea of high dimension n is expressed in the problem or in the methods by which it is approached. For example, the study of probability in Banach spaces gave impetus to a number of methods whose importance has gone far beyond the original goal of extending limit laws to the vector valued case. Familiar applications are in the areas of empirical processes, the use of majorizing measures to study regularly of stochastic processes, and the theory of concentration of measure. Many of the ideas, results and directions of this evolving field were explored on a broad front at the Conference on High Dimensional Probability held at Obwerwolfach in August 1996. This collection of referred papers explores many of the ideas, results and directions in the new field of high dimensional probability, which comprises topics where high dimension plays a key role either in the problems or the methods of approaching them. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. N° de réf. du vendeur 9783764358679

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