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4 produkter
4 produkter
1 596 kr
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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.
Del 1153 - Lecture Notes in Mathematics
Probability in Banach Spaces V
Proceedings of the International Conference held in Medford, USA, July 16-27, 1984
Häftad, Engelska, 1985
483 kr
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1 596 kr
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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.
Beyond The Triangle: Brownian Motion, Ito Calculus, And Fokker-planck Equation - Fractional Generalizations
Inbunden, Engelska, 2018
1 337 kr
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The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker-Planck-Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction.This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students.