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Gaussian Measures In Hilbert Space
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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 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.
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:
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.
Book Synopsis Analysis On Gaussian Spaces by : Yaozhong Hu
Download or read book Analysis On Gaussian Spaces written by Yaozhong Hu and published by World Scientific. This book was released on 2016-08-30 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.
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.
Book Synopsis Gaussian Measures on Separable Hilbert Spaces and Applications by : Stefania Maniglia
Download or read book Gaussian Measures on Separable Hilbert Spaces and Applications written by Stefania Maniglia and published by . This book was released on 2004 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symmetric Hilbert Spaces and Related Topics by : Alain Guichardet
Download or read book Symmetric Hilbert Spaces and Related Topics written by Alain Guichardet and published by Springer. This book was released on 2006-11-15 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
Book Synopsis Stochastic Analysis and Random Maps in Hilbert Space by : A. A. Dorogovtsev
Download or read book Stochastic Analysis and Random Maps in Hilbert Space written by A. A. Dorogovtsev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-01-14 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to stochastic operators in Hilbert space. A number of models in modern probability theory apply the notion of a stochastic operator in explicit or latent form. In this book, objects from the Gaussian case are considered. Therefore, it is useful to consider all random variables and elements as functionals from the Wiener process or its formal derivative, i.e. white noise. The book consists of five chapters. The first chapter is devoted to stochastic calculus and its main goal is to prepare the tools for solving stochastic equations. In the second chapter the structure of stochastic equations, mainly the structure of Gaussian strong linear operators, is studied. In chapter 3 the definition of the action of the stochastic operator on random elements in considered. Chapter 4 deals with the mathematical models in which the notions of stochastic calculus arise and in the final chapter the equation with random operators is considered.
Book Synopsis Statistical Spaces of Gaussian Measures on a Hilbert Space and Their Ellipsoids of Variance by : Timo Koski
Download or read book Statistical Spaces of Gaussian Measures on a Hilbert Space and Their Ellipsoids of Variance written by Timo Koski and published by . This book was released on 1984 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Infinite-Dimensional Gaussian Distributions by : I͡Uriĭ Anatolʹevich Rozanov
Download or read book Infinite-Dimensional Gaussian Distributions written by I͡Uriĭ Anatolʹevich Rozanov and published by American Mathematical Soc.. This book was released on 1971 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Gaussian Processes by : Mikhail Lifshits
Download or read book Lectures on Gaussian Processes written by Mikhail Lifshits and published by Springer Science & Business Media. This book was released on 2012-01-11 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Research Reports written by and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Gaussian Measure of Balls in a Hilbert Space Via Stochastic Integrals by : Richard Michael Bates
Download or read book The Gaussian Measure of Balls in a Hilbert Space Via Stochastic Integrals written by Richard Michael Bates and published by . This book was released on 1980 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Two side estimates for the Gaussian measure of the complements of balls in Hilbert space by : W.-D. Richter
Download or read book Two side estimates for the Gaussian measure of the complements of balls in Hilbert space written by W.-D. Richter and published by . This book was released on 1991 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Vector Space Measures and Applications I by : R.M. Aron
Download or read book Vector Space Measures and Applications I written by R.M. Aron and published by Springer. This book was released on 2006-11-15 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt:
