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Gaussian Hilbert Spaces

1997-06-12 Mathematics
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Release : 1997-06-12
Genre : Mathematics
Kind : eBook
Book Rating : 280/5 ( reviews)

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Book Synopsis Gaussian Hilbert Spaces by : Svante Janson

Download or read book Gaussian Hilbert Spaces written by Svante Janson. This book was released on 1997-06-12. Available in PDF, EPUB and Kindle. Book excerpt: 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

2011-06-28 Business & Economics
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Release : 2011-06-28
Genre : Business & Economics
Kind : eBook
Book Rating : 968/5 ( reviews)

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Book Synopsis Reproducing Kernel Hilbert Spaces in Probability and Statistics by : Alain Berlinet

Download or read book Reproducing Kernel Hilbert Spaces in Probability and Statistics written by Alain Berlinet. This book was released on 2011-06-28. Available in PDF, EPUB and Kindle. Book excerpt: The book covers theoretical questions including the latest extension of the formalism, and computational issues and focuses on some of the more fruitful and promising applications, including statistical signal processing, nonparametric curve estimation, random measures, limit theorems, learning theory and some applications at the fringe between Statistics and Approximation Theory. It is geared to graduate students in Statistics, Mathematics or Engineering, or to scientists with an equivalent level.

Gaussian Measures in Hilbert Space

2020-02-26 Mathematics
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Release : 2020-02-26
Genre : Mathematics
Kind : eBook
Book Rating : 675/5 ( reviews)

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Book Synopsis Gaussian Measures in Hilbert Space by : Alexander Kukush

Download or read book Gaussian Measures in Hilbert Space written by Alexander Kukush. This book was released on 2020-02-26. Available in PDF, EPUB and Kindle. Book excerpt: At the nexus of probability theory, geometry and statistics, a Gaussian measure is constructed on a Hilbert space in two ways: as a product measure and via a characteristic functional based on Minlos-Sazonov theorem. As such, it can be utilized for obtaining results for topological vector spaces. Gaussian Measures contains the proof for Ferniques theorem and its relation to exponential moments in Banach space. Furthermore, the fundamental Feldman-Hájek dichotomy for Gaussian measures in Hilbert space is investigated. Applications in statistics are also outlined. In addition to chapters devoted to measure theory, this book highlights problems related to Gaussian measures in Hilbert and Banach spaces. Borel probability measures are also addressed, with properties of characteristic functionals examined and a proof given based on the classical Banach–Steinhaus theorem. Gaussian Measures is suitable for graduate students, plus advanced undergraduate students in mathematics and statistics. It is also of interest to students in related fields from other disciplines. Results are presented as lemmas, theorems and corollaries, while all statements are proven. Each subsection ends with teaching problems, and a separate chapter contains detailed solutions to all the problems. With its student-tested approach, this book is a superb introduction to the theory of Gaussian measures on infinite-dimensional spaces.

An Introduction to the Theory of Reproducing Kernel Hilbert Spaces

2016-04-11 Mathematics
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Release : 2016-04-11
Genre : Mathematics
Kind : eBook
Book Rating : 092/5 ( reviews)

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Book Synopsis An Introduction to the Theory of Reproducing Kernel Hilbert Spaces by : Vern I. Paulsen

Download or read book An Introduction to the Theory of Reproducing Kernel Hilbert Spaces written by Vern I. Paulsen. This book was released on 2016-04-11. Available in PDF, EPUB and Kindle. Book excerpt: A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.

An Introduction to Infinite-Dimensional Analysis

2006-08-25 Mathematics
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Release : 2006-08-25
Genre : Mathematics
Kind : eBook
Book Rating : 214/5 ( reviews)

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Book Synopsis An Introduction to Infinite-Dimensional Analysis by : Giuseppe Da Prato

Download or read book An Introduction to Infinite-Dimensional Analysis written by Giuseppe Da Prato. This book was released on 2006-08-25. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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