High Dimensional Probability: 43 (Progress in Probability) - Softcover

Softcover

ISBN 10: 3034897901 ISBN 13: 9783034897907

Verlag: Birkhäuser, 2012

Inhaltsangabe

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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Reseña del editor

What is high dimensional probability? Under this broad term one finds 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 regularity of stochastic processes, and the theory of concentration of measure. Many of the new ideas, results and directions of this newly evolving field were explored on a broad front at the Conference on High Dimensional Probability held at Oberwolfach in August 1996. The papers in this volume are marked by vitality and diversity and will give researchers and graduate students in probability or statistics much to whet their interest.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 3034897901
• ISBN 13: 9783034897907
• Einband: Tapa blanda
• Anzahl der Seiten: 348
• Herausgeber: Eberlein Ernst, Hahn Marjorie
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar