Gaussian Hilbert Spaces
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Gaussian Hilbert Spaces
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Author : Svante Janson
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-12
Gaussian Hilbert Spaces written by Svante Janson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-12 with Mathematics categories.
This book treats the very special and fundamental mathematical properties that hold for a family of Gaussian (or normal) random variables. Such random variables have many applications in probability theory, other parts of mathematics, statistics and theoretical physics. The emphasis throughout this book is on the mathematical structures common to all these applications. This will be an excellent resource for all researchers whose work involves random variables.
Reproducing Kernel Hilbert Spaces In Probability And Statistics
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Author : Alain Berlinet
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Reproducing Kernel Hilbert Spaces In Probability And Statistics written by Alain Berlinet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Business & Economics categories.
The reproducing kernel Hilbert space construction is a bijection or transform theory which associates a positive definite kernel (gaussian processes) with a Hilbert space offunctions. Like all transform theories (think Fourier), problems in one space may become transparent in the other, and optimal solutions in one space are often usefully optimal in the other. The theory was born in complex function theory, abstracted and then accidently injected into Statistics; Manny Parzen as a graduate student at Berkeley was given a strip of paper containing his qualifying exam problem- It read "reproducing kernel Hilbert space"- In the 1950's this was a truly obscure topic. Parzen tracked it down and internalized the subject. Soon after, he applied it to problems with the following fla vor: consider estimating the mean functions of a gaussian process. The mean functions which cannot be distinguished with probability one are precisely the functions in the Hilbert space associated to the covariance kernel of the processes. Parzen's own lively account of his work on re producing kernels is charmingly told in his interview with H. Joseph Newton in Statistical Science, 17, 2002, p. 364-366. Parzen moved to Stanford and his infectious enthusiasm caught Jerry Sacks, Don Ylvisaker and Grace Wahba among others. Sacks and Ylvis aker applied the ideas to design problems such as the following. Sup pose (XdO
Symmetric Hilbert Spaces And Related Topics
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Author : Alain Guichardet
language : en
Publisher: Springer
Release Date : 2006-11-15
Symmetric Hilbert Spaces And Related Topics written by Alain Guichardet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
An Introduction To Infinite Dimensional Analysis
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Author : Giuseppe Da Prato
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-25
An Introduction To Infinite Dimensional Analysis written by Giuseppe Da Prato and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-25 with Mathematics categories.
Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.
Gaussian Processes Function Theory And The Inverse Spectral Problem
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Author : Harry Dym
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
Gaussian Processes Function Theory And The Inverse Spectral Problem written by Harry Dym and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
This text offers background in function theory, Hardy functions, and probability as preparation for surveys of Gaussian processes, strings and spectral functions, and strings and spaces of integral functions. It addresses the relationship between the past and the future of a real, one-dimensional, stationary Gaussian process. 1976 edition.
Functional Analysis For Probability And Stochastic Processes
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Author : Adam Bobrowski
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-11
Functional Analysis For Probability And Stochastic Processes written by Adam Bobrowski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-11 with Mathematics categories.
This text presents selected areas of functional analysis that can facilitate an understanding of ideas in probability and stochastic processes. Topics covered include basic Hilbert and Banach spaces, weak topologies and Banach algebras, and the theory ofsemigroups of bounded linear operators.
Lectures On Gaussian Processes
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Author : Mikhail Lifshits
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-11
Lectures On Gaussian Processes written by Mikhail Lifshits and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-11 with Mathematics categories.
Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.
Mathematical Analysis And Applications
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Author : Michael Ruzhansky
language : en
Publisher: John Wiley & Sons
Release Date : 2018-04-11
Mathematical Analysis And Applications written by Michael Ruzhansky and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-11 with Mathematics categories.
An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.
Factorization Of Linear Operators And Geometry Of Banach Spaces
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Author : Gilles Pisier
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Factorization Of Linear Operators And Geometry Of Banach Spaces written by Gilles Pisier and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
"Expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25-29, 1984"--T.p. verso.