Gaussian Hilbert Spaces PDF Download
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Author | : Svante Janson |
Publisher | : Cambridge University Press |
Total Pages | : 358 |
Release | : 1997-06-12 |
Genre | : Mathematics |
ISBN | : 0521561280 |
Download Gaussian Hilbert Spaces Book in PDF, ePub and Kindle
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.
Author | : Alain Berlinet |
Publisher | : Springer Science & Business Media |
Total Pages | : 369 |
Release | : 2011-06-28 |
Genre | : Business & Economics |
ISBN | : 1441990968 |
Download Reproducing Kernel Hilbert Spaces in Probability and Statistics Book in PDF, ePub and Kindle
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.
Author | : Alexander Kukush |
Publisher | : John Wiley & Sons |
Total Pages | : 272 |
Release | : 2020-02-26 |
Genre | : Mathematics |
ISBN | : 1786302675 |
Download Gaussian Measures in Hilbert Space Book in PDF, ePub and Kindle
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.
Author | : Vidyadhar S. Mandrekar |
Publisher | : CRC Press |
Total Pages | : 200 |
Release | : 2015-06-23 |
Genre | : Mathematics |
ISBN | : 1498707823 |
Download Stochastic Analysis for Gaussian Random Processes and Fields Book in PDF, ePub and Kindle
Stochastic Analysis for Gaussian Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it studies Gaussian random fields using reproducing kernel Hilbert spaces (RKHSs).The book begins with preliminary results on covariance and associated RKHS
Author | : Alain Guichardet |
Publisher | : Springer |
Total Pages | : 203 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540374558 |
Download Symmetric Hilbert Spaces and Related Topics Book in PDF, ePub and Kindle
Author | : Harry Dym |
Publisher | : Courier Corporation |
Total Pages | : 354 |
Release | : 2008-01-01 |
Genre | : Mathematics |
ISBN | : 048646279X |
Download Gaussian Processes, Function Theory, and the Inverse Spectral Problem Book in PDF, ePub and Kindle
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.
Author | : Giuseppe Da Prato |
Publisher | : Springer Science & Business Media |
Total Pages | : 217 |
Release | : 2006-08-25 |
Genre | : Mathematics |
ISBN | : 3540290214 |
Download An Introduction to Infinite-Dimensional Analysis Book in PDF, ePub and Kindle
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.
Author | : Giuseppe Da Prato |
Publisher | : Cambridge University Press |
Total Pages | : 206 |
Release | : 2002-07-25 |
Genre | : Mathematics |
ISBN | : 9780521777292 |
Download Second Order Partial Differential Equations in Hilbert Spaces Book in PDF, ePub and Kindle
Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.
Author | : Stefania Maniglia |
Publisher | : |
Total Pages | : 85 |
Release | : 2004 |
Genre | : |
ISBN | : |
Download Gaussian Measures on Separable Hilbert Spaces and Applications Book in PDF, ePub and Kindle
Author | : Yaozhong Hu |
Publisher | : World Scientific |
Total Pages | : 483 |
Release | : 2016-08-30 |
Genre | : Mathematics |
ISBN | : 9813142197 |
Download Analysis On Gaussian Spaces Book in PDF, ePub and Kindle
'Written by a well-known expert in fractional stochastic calculus, this book offers a comprehensive overview of Gaussian analysis, with particular emphasis on nonlinear Gaussian functionals. In addition, it covers some topics that are not frequently encountered in other treatments, such as Littlewood-Paley-Stein, etc. This coverage makes the book a valuable addition to the literature. Many results presented in this book were hitherto available only in the research literature in the form of research papers by the author and his co-authors.'Mathematical Reviews ClippingsAnalysis of functions on the finite dimensional Euclidean space with respect to the Lebesgue measure is fundamental in mathematics. The extension to infinite dimension is a great challenge due to the lack of Lebesgue measure on infinite dimensional space. Instead the most popular measure used in infinite dimensional space is the Gaussian measure, which has been unified under the terminology of 'abstract Wiener space'.Out of the large amount of work on this topic, this book presents some fundamental results plus recent progress. We shall present some results on the Gaussian space itself such as the Brunn-Minkowski inequality, Small ball estimates, large tail estimates. The majority part of this book is devoted to the analysis of nonlinear functions on the Gaussian space. Derivative, Sobolev spaces are introduced, while the famous Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood-Paley-Stein-Meyer theory are given in details.This book includes some basic material that cannot be found elsewhere that the author believes should be an integral part of the subject. For example, the book includes some interesting and important inequalities, the Littlewood-Paley-Stein-Meyer theory, and the Hörmander theorem. The book also includes some recent progress achieved by the author and collaborators on density convergence, numerical solutions, local times.