Gaussian Measures In Finite And Infinite Dimensions
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Gaussian Measures In Finite And Infinite Dimensions
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Author : Daniel W. Stroock
language : en
Publisher:
Release Date : 2023
Gaussian Measures In Finite And Infinite Dimensions written by Daniel W. Stroock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
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.
Gaussian Measures
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Author : Vladimir I. Bogachev
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-01-26
Gaussian Measures written by Vladimir I. Bogachev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-26 with categories.
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.
Analysis On Gaussian Spaces
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Author : Yaozhong Hu
language : en
Publisher: World Scientific
Release Date : 2016-08-30
Analysis On Gaussian Spaces written by Yaozhong Hu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-30 with Mathematics categories.
Analysis 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.
Gaussian Measures In Finite And Infinite Dimensions
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Author : Daniel W. Stroock
language : en
Publisher: Springer Nature
Release Date : 2023-02-15
Gaussian Measures In Finite And Infinite Dimensions written by Daniel W. Stroock and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-15 with Mathematics categories.
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.
Gaussian Measures In Hilbert Space
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Author : Alexander Kukush
language : en
Publisher: John Wiley & Sons
Release Date : 2020-02-26
Gaussian Measures In Hilbert Space written by Alexander Kukush and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-26 with Mathematics categories.
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.
Measure And Integration Theory On Infinite Dimensional Spaces
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Author :
language : en
Publisher: Academic Press
Release Date : 1972-10-16
Measure And Integration Theory On Infinite Dimensional Spaces written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-10-16 with Mathematics categories.
Measure and Integration Theory on Infinite-Dimensional Spaces
Finite And Infinite Dimensional Analysis In Honor Of Leonard Gross
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Author : Hui-Hsiung Kuo
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Finite And Infinite Dimensional Analysis In Honor Of Leonard Gross written by Hui-Hsiung Kuo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book contains the proceedings of the special session in honor of Leonard Gross held at the annual Joint Mathematics Meetings in New Orleans (LA). The speakers were specialists in a variety of fields, and many were Professor Gross's former Ph.D. students and their descendants. Papers in this volume present results from several areas of mathematics. They illustrate applications of powerful ideas that originated in Gross's work and permeate diverse fields. Topics include stochastic partial differential equations, white noise analysis, Brownian motion, Segal-Bargmann analysis, heat kernels, and some applications. The volume should be useful to graduate students and researchers. It provides perspective on current activity and on central ideas and techniques in the topics covered.
Infinite Dimensional Gaussian Distributions
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Author : I͡Uriĭ Anatolʹevich Rozanov
language : en
Publisher: American Mathematical Soc.
Release Date : 1971
Infinite Dimensional Gaussian Distributions written by I͡Uriĭ Anatolʹevich Rozanov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Distribution (Probability theory) categories.
Sums And Gaussian Vectors
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Author : Vadim Yurinsky
language : en
Publisher: Springer
Release Date : 2006-11-14
Sums And Gaussian Vectors written by Vadim Yurinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
Spectral Methods In Infinite Dimensional Analysis 1 1995
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Author : I︠U︡riĭ Makarovich Berezanskiĭ
language : en
Publisher: Springer Science & Business Media
Release Date : 1994
Spectral Methods In Infinite Dimensional Analysis 1 1995 written by I︠U︡riĭ Makarovich Berezanskiĭ and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Degree of freedom categories.