Gaussian Measures On Separable Hilbert Spaces And Applications PDF Download
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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 | : 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 | : Vladimir I. Bogachev |
Publisher | : American Mathematical Soc. |
Total Pages | : 450 |
Release | : 2015-01-26 |
Genre | : Mathematics |
ISBN | : 147041869X |
Download Gaussian Measures Book in PDF, ePub and Kindle
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.
Author | : Daniel W. Stroock |
Publisher | : Springer Nature |
Total Pages | : 152 |
Release | : 2023-02-15 |
Genre | : Mathematics |
ISBN | : 3031231228 |
Download Gaussian Measures in Finite and Infinite Dimensions Book in PDF, ePub and Kindle
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.
Author | : R.M. Aron |
Publisher | : Springer |
Total Pages | : 463 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540359060 |
Download Vector Space Measures and Applications I Book in PDF, ePub and Kindle
Author | : Howard L. Weinert |
Publisher | : |
Total Pages | : 680 |
Release | : 1982 |
Genre | : Mathematics |
ISBN | : |
Download Reproducing Kernel Hilbert Spaces 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.
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 | : Richard M. Aron |
Publisher | : Springer |
Total Pages | : 476 |
Release | : 1978 |
Genre | : Measure theory |
ISBN | : |
Download Vector Space Measures and Applications Book in PDF, ePub and Kindle
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