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The Generic Chaining [electronic resource] :Upper and Lower Bounds of Stochastic Processes / by Michel Talagrand.

by Talagrand, Michel [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Springer Monographs in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.Description: VIII, 222 p. online resource.ISBN: 9783540274995.Subject(s): Mathematics | Distribution (Probability theory) | Statistics | Mathematics | Probability Theory and Stochastic Processes | Approximations and Expansions | Statistics for Engineering, Physics, Computer Science, Chemistry & GeosciencesDDC classification: 519.2 Online resources: Click here to access online
Contents:
Overview and Basic Facts -- Gaussian Processes and Related Structures -- Matching Theorems -- The Bernoulli Conjecture -- Families of distances -- Applications to Banach Space Theory.
In: Springer eBooksSummary: The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After essential contributions by R. Dudley and X. Fernique, it was solved by the author in 1985. This advance was followed by a great improvement of our understanding of the boundedness of other fundamental classes of processes (empirical processes, infinitely divisible processes, etc.) This challenging body of work has now been considerably simplified through the notion of "generic chaining", a completely natural variation on the ideas of Kolmogorov. The entirely new presentation adopted here takes the reader from the first principles to the edge of current knowledge, and to the wonderful open problems that remain in this domain.
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Overview and Basic Facts -- Gaussian Processes and Related Structures -- Matching Theorems -- The Bernoulli Conjecture -- Families of distances -- Applications to Banach Space Theory.

The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After essential contributions by R. Dudley and X. Fernique, it was solved by the author in 1985. This advance was followed by a great improvement of our understanding of the boundedness of other fundamental classes of processes (empirical processes, infinitely divisible processes, etc.) This challenging body of work has now been considerably simplified through the notion of "generic chaining", a completely natural variation on the ideas of Kolmogorov. The entirely new presentation adopted here takes the reader from the first principles to the edge of current knowledge, and to the wonderful open problems that remain in this domain.

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