[PDF] Full Gaussian Measures In Hilbert Space Download eBook

Gaussian Measures in Hilbert Space

Author: Alexander Kukush

Publisher: John Wiley & Sons

Published: 2020-02-26

Total Pages: 272

ISBN-13: 1786302675

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.

Gaussian Hilbert Spaces

Author: Svante Janson

Publisher: Cambridge University Press

Published: 1997-06-12

Total Pages: 358

ISBN-13: 0521561280

DOWNLOAD EBOOK

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.

An Introduction to Infinite-Dimensional Analysis

Author: Giuseppe Da Prato

Publisher: Springer Science & Business Media

Published: 2006-08-25

Total Pages: 217

ISBN-13: 3540290214

DOWNLOAD EBOOK

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.

Reproducing Kernel Hilbert Spaces in Probability and Statistics

Author: Alain Berlinet

Publisher: Springer Science & Business Media

Published: 2011-06-28

Total Pages: 369

ISBN-13: 1441990968

DOWNLOAD EBOOK

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

Author: Vladimir I. Bogachev

Publisher: American Mathematical Soc.

Published: 2015-01-26

Total Pages: 450

ISBN-13: 147041869X

DOWNLOAD EBOOK

This book gives a systematic exposition of the modern theory of Gaussian measures. It presents with complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes. Suitable for use as a graduate text and/or a reference work, this volume contains many examples, exercises, and an extensive bibliography. It brings together many results that have not appeared previously in book form.

Mathematical Analysis and Applications

Author: Michael Ruzhansky

Publisher: John Wiley & Sons

Published: 2018-04-11

Total Pages: 1021

ISBN-13: 1119414334

DOWNLOAD EBOOK

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.

Gaussian Measures in Banach Spaces

Author: H.-H. Kuo

Publisher: Springer

Published: 2006-11-14

Total Pages: 230

ISBN-13: 3540375082

DOWNLOAD EBOOK

Inequalities

Author: Elliott H. Lieb

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 687

ISBN-13: 3642559255

DOWNLOAD EBOOK

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.