Measures On Infinite Dimensional Spaces
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Measures On Infinite Dimensional Spaces
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Author : Yasuo Yamasaki
language : en
Publisher: World Scientific
Release Date : 1985
Measures On Infinite Dimensional Spaces written by Yasuo Yamasaki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Science categories.
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.
Measures On Infinite Dimensional Spaces
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Author : Yasuo Yamasaki
language : en
Publisher:
Release Date : 1982
Measures On Infinite Dimensional Spaces written by Yasuo Yamasaki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Dimensional analysis categories.
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
Measure And Integration Theory On Infinite Dimensional Spaces
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Author : Dao-xing Xia
language : en
Publisher:
Release Date : 1972
Measure And Integration Theory On Infinite Dimensional Spaces written by Dao-xing Xia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Generalized spaces categories.
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.
Invariant And Quasiinvariant Measures In Infinite Dimensional Topological Vector Spaces
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Author : Gogi Pantsulaia
language : en
Publisher:
Release Date : 2007
Invariant And Quasiinvariant Measures In Infinite Dimensional Topological Vector Spaces written by Gogi Pantsulaia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Ergodic theory categories.
This monograph deals with certain aspects of the general theory of systems. The author develops the ergodic theory, which is the theory of quaslinvariant and invariant measures in such infinite-dimensional vector spaces which appear as models of various (physical, economic, genetic, linguistic, social, etc.) processes. The methods of ergodic theory are successful as applied to study properties of such systems. A foundation for ergodic theory was stimulated by the necessity of a consideration of statistic mechanic problems and was directly connected with the works of G. Birkhoff, Kryloff and Bogoliuboff, E. Hoph and other famous mathematicians.
Differentiable Measures And The Malliavin Calculus
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Author : Vladimir Igorevich Bogachev
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-07-21
Differentiable Measures And The Malliavin Calculus written by Vladimir Igorevich 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 2010-07-21 with Mathematics categories.
This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.
Measures And Differential Equations In Infinite Dimensional Space
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Author : IUrii Lvovich Daletskii
language : en
Publisher: Springer
Release Date : 1991
Measures And Differential Equations In Infinite Dimensional Space written by IUrii Lvovich Daletskii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
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.
Convex Measures On Infinite Dimensional Vector Spaces
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Author : Christer Borell
language : en
Publisher:
Release Date : 1974
Convex Measures On Infinite Dimensional Vector Spaces written by Christer Borell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.