Gaussian Measures In Hilbert Space

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Gaussian Measures in Hilbert Space

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Author : Alexander Kukush
Publisher : John Wiley & Sons
ISBN 13 : 1786302675
Total Pages : 272 pages
Book Rating : 4.7/5 (863 download)

Book Synopsis Gaussian Measures in Hilbert Space by : Alexander Kukush

Download or read book Gaussian Measures in Hilbert Space written by Alexander Kukush and published by John Wiley & Sons. This book was released on 2020-02-26 with total page 272 pages. 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.

Gaussian Hilbert Spaces

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Author : Svante Janson
Publisher : Cambridge University Press
ISBN 13 : 0521561280
Total Pages : 358 pages
Book Rating : 4.5/5 (215 download)

Book Synopsis Gaussian Hilbert Spaces by : Svante Janson

Download or read book Gaussian Hilbert Spaces written by Svante Janson and published by Cambridge University Press. This book was released on 1997-06-12 with total page 358 pages. 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.

Gaussian Measures

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Author : Vladimir I. Bogachev
Publisher : American Mathematical Soc.
ISBN 13 : 147041869X
Total Pages : 450 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis Gaussian Measures by : Vladimir I. Bogachev

Download or read book Gaussian Measures written by Vladimir I. Bogachev and published by American Mathematical Soc.. This book was released on 2015-01-26 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Infinite-Dimensional Analysis

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Author : Giuseppe Da Prato
Publisher : Springer Science & Business Media
ISBN 13 : 3540290214
Total Pages : 217 pages
Book Rating : 4.5/5 (42 download)

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 and published by Springer Science & Business Media. This book was released on 2006-08-25 with total page 217 pages. 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.

Reproducing Kernel Hilbert Spaces in Probability and Statistics

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Author : Alain Berlinet
Publisher : Springer Science & Business Media
ISBN 13 : 1441990968
Total Pages : 369 pages
Book Rating : 4.4/5 (419 download)

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 and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 369 pages. 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.

Mathematical Analysis and Applications

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Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414334
Total Pages : 1021 pages
Book Rating : 4.1/5 (194 download)

Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1021 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Author : H.-H. Kuo
Publisher : Springer
ISBN 13 : 3540375082
Total Pages : 230 pages
Book Rating : 4.5/5 (43 download)

Book Synopsis Gaussian Measures in Banach Spaces by : H.-H. Kuo

Download or read book Gaussian Measures in Banach Spaces written by H.-H. Kuo and published by Springer. This book was released on 2006-11-14 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inequalities

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Author : Elliott H. Lieb
Publisher : Springer Science & Business Media
ISBN 13 : 3642559255
Total Pages : 687 pages
Book Rating : 4.6/5 (425 download)

Book Synopsis Inequalities by : Elliott H. Lieb

Download or read book Inequalities written by Elliott H. Lieb and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Kazhdan's Property (T)

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Author : Bekka M Bachir La Harpe Pierre de Valette Alain
Publisher :
ISBN 13 : 9780511395116
Total Pages : 488 pages
Book Rating : 4.3/5 (951 download)

Book Synopsis Kazhdan's Property (T) by : Bekka M Bachir La Harpe Pierre de Valette Alain

Download or read book Kazhdan's Property (T) written by Bekka M Bachir La Harpe Pierre de Valette Alain and published by . This book was released on 2014-05-14 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to the role of Property (T), with applications to an amazing number of fields within mathematics.

Gaussian Measures in Finite and Infinite Dimensions

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Author : Daniel W. Stroock
Publisher : Springer Nature
ISBN 13 : 3031231228
Total Pages : 152 pages
Book Rating : 4.0/5 (312 download)

Book Synopsis Gaussian Measures in Finite and Infinite Dimensions by : Daniel W. Stroock

Download or read book Gaussian Measures in Finite and Infinite Dimensions written by Daniel W. Stroock and published by Springer Nature. This book was released on 2023-02-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a concise introduction, suitable for a one-semester special topicscourse, to the remarkable properties of Gaussian measures on both finite and infinitedimensional spaces. It begins with a brief resumé of probabilistic results in which Fourieranalysis plays an essential role, and those results are then applied to derive a few basicfacts about Gaussian measures on finite dimensional spaces. In anticipation of the analysisof Gaussian measures on infinite dimensional spaces, particular attention is given to those/divproperties of Gaussian measures that are dimension independent, and Gaussian processesare constructed. The rest of the book is devoted to the study of Gaussian measures onBanach spaces. The perspective adopted is the one introduced by I. Segal and developedby L. Gross in which the Hilbert structure underlying the measure is emphasized.The contents of this book should be accessible to either undergraduate or graduate/divstudents who are interested in probability theory and have a solid background in Lebesgueintegration theory and a familiarity with basic functional analysis. Although the focus ison Gaussian measures, the book introduces its readers to techniques and ideas that haveapplications in other contexts.

Spectral Methods in Infinite-Dimensional Analysis

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Author : Yu.M. Berezansky
Publisher : Springer Science & Business Media
ISBN 13 : 940110509X
Total Pages : 983 pages
Book Rating : 4.4/5 (11 download)

Book Synopsis Spectral Methods in Infinite-Dimensional Analysis by : Yu.M. Berezansky

Download or read book Spectral Methods in Infinite-Dimensional Analysis written by Yu.M. Berezansky and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 983 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Russian edition of this book appeared 5 years ago. Since that time, many results have been improved upon and new approaches to the problems investigated in the book have appeared. But the greatest surprise for us was to discover that there exists a large group of mathematicians working in the area of the so-called White Noise Analysis which is closely connected with the essential part of our book, namely, with the theory of generalized functions of infinitely many variables. The first papers dealing with White Noise Analysis were written by T. Hida in Japan in 1975. Later, this analysis was devel oped intensively in Japan, Germany, U.S.A., Taipei, and in other places. The related problems of infinite-dimensional analysis have been studied in Kiev since 1967, and the theory of generalized functions of infinitely many variables has been in vestigated since 1973. However, due to the political system in the U.S.S.R., contact be tween Ukrainian and foreign mathematicians was impossible for a long period of time. This is why, to our great regret, only at the end of 1988 did one of the authors meet L. Streit who told him about the existence of White Noise Analysis. And it become clear that many results in these two theories coincide and that, in fact, there exists a single theory and not two distinct ones.

Spectral methods in infinite-dimensional analysis. 1 (1995)

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Author : I︠U︡riĭ Makarovich Berezanskiĭ
Publisher : Springer Science & Business Media
ISBN 13 : 9780792328476
Total Pages : 600 pages
Book Rating : 4.3/5 (284 download)

Book Synopsis Spectral methods in infinite-dimensional analysis. 1 (1995) by : I︠U︡riĭ Makarovich Berezanskiĭ

Download or read book Spectral methods in infinite-dimensional analysis. 1 (1995) written by I︠U︡riĭ Makarovich Berezanskiĭ and published by Springer Science & Business Media. This book was released on 1994 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Lévy Laplacian

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Author : M. N. Feller
Publisher :
ISBN 13 : 0511131445
Total Pages : 161 pages
Book Rating : 4.5/5 (111 download)

Book Synopsis The Lévy Laplacian by : M. N. Feller

Download or read book The Lévy Laplacian written by M. N. Feller and published by . This book was released on 2005-11-13 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text was the first book on the Lévy Laplacian that generalized classical work and could be widely applied.

Gradient Flows

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Author : Luigi Ambrosio
Publisher : Springer Science & Business Media
ISBN 13 : 376438722X
Total Pages : 333 pages
Book Rating : 4.7/5 (643 download)

Book Synopsis Gradient Flows by : Luigi Ambrosio

Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-10-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.

Spectral methods in infinite-dimensional analysis. 2 (1995)

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Author : I︠U︡riĭ Makarovich Berezanskiĭ
Publisher : Springer Science & Business Media
ISBN 13 : 9780792328483
Total Pages : 448 pages
Book Rating : 4.3/5 (284 download)

Book Synopsis Spectral methods in infinite-dimensional analysis. 2 (1995) by : I︠U︡riĭ Makarovich Berezanskiĭ

Download or read book Spectral methods in infinite-dimensional analysis. 2 (1995) written by I︠U︡riĭ Makarovich Berezanskiĭ and published by Springer Science & Business Media. This book was released on 1995 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Measures on Infinite Dimensional Spaces

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Author : Yasuo Yamasaki
Publisher : World Scientific
ISBN 13 : 9789971978525
Total Pages : 276 pages
Book Rating : 4.9/5 (785 download)

Book Synopsis Measures on Infinite Dimensional Spaces by : Yasuo Yamasaki

Download or read book Measures on Infinite Dimensional Spaces written by Yasuo Yamasaki and published by World Scientific. This book was released on 1985 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at Yale and Kyoto Universities and provides a self-contained detailed exposition of the following subjects: 1) The construction of infinite dimensional measures, 2) Invariance and quasi-invariance of measures under translations. This book furnishes an important tool for the analysis of physical systems with infinite degrees of freedom (such as field theory, statistical physics and field dynamics) by providing material on the foundations of these problems.

Geometric Problems in the Theory of Infinite-dimensional Probability Distributions

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Author : V. N. Sudakov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821830413
Total Pages : 188 pages
Book Rating : 4.8/5 (34 download)

Book Synopsis Geometric Problems in the Theory of Infinite-dimensional Probability Distributions by : V. N. Sudakov

Download or read book Geometric Problems in the Theory of Infinite-dimensional Probability Distributions written by V. N. Sudakov and published by American Mathematical Soc.. This book was released on 1979 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses problems in the distribution theory of probability.