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Author : H.-H. Kuo
Publisher : Springer
ISBN 13 : 3540375082
Total Pages : 230 pages
Book Rating : 4.5/5 (43 download)
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:
Author : Hui-Hsiung Kuo
Publisher : CreateSpace
ISBN 13 : 9781419645808
Total Pages : 232 pages
Book Rating : 4.6/5 (458 download)
Download or read book Gaussian Measures in Banach Spaces written by Hui-Hsiung Kuo and published by CreateSpace. This book was released on 2006-06-29 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexander Kukush
Publisher : John Wiley & Sons
ISBN 13 : 1786302675
Total Pages : 272 pages
Book Rating : 4.7/5 (863 download)
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.
Author : Vladimir I. Bogachev
Publisher : American Mathematical Soc.
ISBN 13 : 147041869X
Total Pages : 450 pages
Book Rating : 4.4/5 (74 download)
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.
Author : Yaozhong Hu
Publisher : World Scientific
ISBN 13 : 9813142197
Total Pages : 483 pages
Book Rating : 4.8/5 (131 download)
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.
Author : Benedikt Wilbertz
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (118 download)
Download or read book Construction of Optimal Quantizers for Gaussian Measures on Banach Spaces written by Benedikt Wilbertz and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michel Ledoux
Publisher : Springer Science & Business Media
ISBN 13 : 3642202128
Total Pages : 493 pages
Book Rating : 4.6/5 (422 download)
Download or read book Probability in Banach Spaces written by Michel Ledoux and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
Author : 范君豪
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (713 download)
Download or read book Characterization of Gaussian Measure on Banach Space written by 范君豪 and published by . This book was released on 2008 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniel Li
Publisher : Cambridge University Press
ISBN 13 : 1107162629
Total Pages : 405 pages
Book Rating : 4.1/5 (71 download)
Download or read book Introduction to Banach Spaces: Analysis and Probability written by Daniel Li and published by Cambridge University Press. This book was released on 2018 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of a two-volume overview focuses on the applications of Banach spaces and recent developments in the field.
Author : Alejandro Daniel De Acosta
Publisher :
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4.:/5 (29 download)
Download or read book Existence and Convergence of Probability Measures in Banach Spaces written by Alejandro Daniel De Acosta and published by . This book was released on 1969 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Charles R. Baker
Publisher :
ISBN 13 :
Total Pages : 66 pages
Book Rating : 4.:/5 (128 download)
Download or read book Zero-One Laws for Gaussian Measures on Banach Space written by Charles R. Baker and published by . This book was released on 1971 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let Beta be a real separable Banach space, mu a Gaussian measure on the Borel sigma-field of Beta, and B sub mu (Beta) the completion of the Borel sigma-field under mu. If G belongs to B sub mu (Beta) is a subgroup, it is shown that mu(G) = 0 or 1, extending a result due to Kallianpur and Jain. Necessary and sufficient conditions are given for mu(G) = 1 for the case where G is the range of a bounded linear operator. These results are then applied to obtain a number of 0-1 statements for the sample functions properties of a Gaussian stochastic process. The zero-one law is then extended to a class of non-Gaussian measures, and applications are given to some non-Gaussian stochastic processes. (Author).
Author : R.M. Dudley
Publisher : Springer Science & Business Media
ISBN 13 : 1461203678
Total Pages : 512 pages
Book Rating : 4.4/5 (612 download)
Download or read book Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference written by R.M. Dudley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly.
Author : Daniel W. Stroock
Publisher :
ISBN 13 : 9783031231230
Total Pages : 0 pages
Book Rating : 4.2/5 (312 download)
Download or read book Gaussian Measures in Finite and Infinite Dimensions written by Daniel W. Stroock and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a concise introduction, suitable for a one-semester special topics course, to the remarkable properties of Gaussian measures on both finite and infinite dimensional spaces. It begins with a brief resumé of probabilistic results in which Fourier analysis plays an essential role, and those results are then applied to derive a few basic facts about Gaussian measures on finite dimensional spaces. In anticipation of the analysis of Gaussian measures on infinite dimensional spaces, particular attention is given to those properties of Gaussian measures that are dimension independent, and Gaussian processes are constructed. The rest of the book is devoted to the study of Gaussian measures on Banach spaces. The perspective adopted is the one introduced by I. Segal and developed by 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 students who are interested in probability theory and have a solid background in Lebesgue integration theory and a familiarity with basic functional analysis. Although the focus is on Gaussian measures, the book introduces its readers to techniques and ideas that have applications in other contexts.
Author : Anatole Beck
Publisher : Springer
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.3/5 (91 download)
Download or read book Probability in Banach Spaces IV written by Anatole Beck and published by Springer. This book was released on 1983 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gholamhossein Gharagoz Hamedani
Publisher :
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.3/5 (129 download)
Download or read book Inversion Formulae for the Probability Measures on Banach Spaces written by Gholamhossein Gharagoz Hamedani and published by . This book was released on 1971 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John Mathieson
Publisher :
ISBN 13 :
Total Pages : 114 pages
Book Rating : 4.3/5 (129 download)
Download or read book Probability Measures on Real Separable Banach Spaces written by John Mathieson and published by . This book was released on 1974 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James Kuelbs
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (3 download)
Download or read book On the Equivalence of Gaussian Measures Related to Banach Space-Valued Processes written by James Kuelbs and published by . This book was released on 1972 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the theory of operator-valued reproducing kernels a necessary and sufficient condition for equivalence or singularity of two Gaussian measures corresponding to a Banach space-valued stochastic processes is given. The characterization is in terms of operator-valued covariance kernels associated with these measures. The result is applied to the Wiener process with a Banach state space and an infinite dimensional extension of a result of Shepp is obtained. (Author).
