Gaussian Measures

Author : Vladimir I. Bogachev
Publisher : American Mathematical Soc.
Page : 433 pages
File Size : 46,5 Mb
Release : 2015-01-26
Category : Electronic
ISBN : 9781470418694

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Gaussian Measures by Vladimir I. Bogachev Pdf

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 : Alexander Kukush
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 54,8 Mb
Release : 2020-02-26
Category : Mathematics
ISBN : 9781786302670

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Gaussian Measures in Hilbert Space by Alexander Kukush Pdf

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 : Daniel W. Stroock
Publisher : Springer Nature
Page : 152 pages
File Size : 47,9 Mb
Release : 2023-02-15
Category : Mathematics
ISBN : 9783031231223

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Gaussian Measures in Finite and Infinite Dimensions by Daniel W. Stroock Pdf

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 : H.-H. Kuo
Publisher : Springer
Page : 230 pages
File Size : 48,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540375081

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Gaussian Measures in Banach Spaces by H.-H. Kuo Pdf

Author : Svante Janson
Publisher : Cambridge University Press
Page : 358 pages
File Size : 52,6 Mb
Release : 1997-06-12
Category : Mathematics
ISBN : 9780521561280

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Gaussian Hilbert Spaces by Svante Janson Pdf

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.

Author : M.A. Lifshits
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 51,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401584746

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Gaussian Random Functions by M.A. Lifshits Pdf

It is well known that the normal distribution is the most pleasant, one can even say, an exemplary object in the probability theory. It combines almost all conceivable nice properties that a distribution may ever have: symmetry, stability, indecomposability, a regular tail behavior, etc. Gaussian measures (the distributions of Gaussian random functions), as infinite-dimensional analogues of tht

Author : I͡Uriĭ Anatolʹevich Rozanov
Publisher : American Mathematical Soc.
Page : 172 pages
File Size : 47,9 Mb
Release : 1971
Category : Distribution (Probability theory)
ISBN : 0821830082

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Infinite-Dimensional Gaussian Distributions by I͡Uriĭ Anatolʹevich Rozanov Pdf

Author : Wilfredo Urbina-Romero
Publisher : Springer
Page : 477 pages
File Size : 50,8 Mb
Release : 2019-06-21
Category : Mathematics
ISBN : 9783030055974

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Gaussian Harmonic Analysis by Wilfredo Urbina-Romero Pdf

Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: harmonic analysis and probability. The book is intended for a very diverse audience, from graduate students all the way to researchers working in a broad spectrum of areas in analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of real analysis as well as with classical harmonic analysis, including Calderón-Zygmund theory; also some knowledge of basic orthogonal polynomials theory would be convenient. The monograph develops the main topics of classical harmonic analysis (semigroups, covering lemmas, maximal functions, Littlewood-Paley functions, spectral multipliers, fractional integrals and fractional derivatives, singular integrals) with respect to the Gaussian measure. The text provide an updated exposition, as self-contained as possible, of all the topics in Gaussian harmonic analysis that up to now are mostly scattered in research papers and sections of books; also an exhaustive bibliography for further reading. Each chapter ends with a section of notes and further results where connections between Gaussian harmonic analysis and other connected fields, points of view and alternative techniques are given. Mathematicians and researchers in several areas will find the breadth and depth of the treatment of the subject highly useful.

Author : Houman Owhadi,Clint Scovel
Publisher : Cambridge University Press
Page : 491 pages
File Size : 43,8 Mb
Release : 2019-10-24
Category : Mathematics
ISBN : 9781108484367

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Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization by Houman Owhadi,Clint Scovel Pdf

Presents interplays between numerical approximation and statistical inference as a pathway to simple solutions to fundamental problems.

Author : Catherine Donati Martin,Antoine Lejay,Alain Rouault
Publisher : Springer
Page : 503 pages
File Size : 54,6 Mb
Release : 2010-10-20
Category : Mathematics
ISBN : 9783642152177

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Séminaire de Probabilités XLIII by Catherine Donati Martin,Antoine Lejay,Alain Rouault Pdf

This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.

Author : Takeyuki Hida
Publisher : World Scientific
Page : 392 pages
File Size : 51,6 Mb
Release : 1995-01-10
Category : Stochastic processes
ISBN : 9789814550970

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Mathematical Approach to Fluctuations by Takeyuki Hida Pdf

Contents:Trace Formulae for Levy-Gaussian Measures and Their Application (L Accardi & O G Smolyanov)Mathematical Theory of Early Vision: Historical Note (J J Atick)Unidirectional versus Bi-directional Theory for Trajectory Planning and Control (M Kawato)Relaxations in the Electronic Excited States of Complex Systems (T Kushida)Coherent Approach to Fluctuations (M Suzuki)Simulational and Analytic Studies of Anomalous Relaxation in Disordered Systems (F Yonezawa et al)Work with Pavel Bleher on Eigenvalue Statistics in Integrable Dynamical Systems (F Dyson)and other papers Readership: Applied mathematicians.keywords:

Author : Library of Congress
Publisher : Unknown
Page : 1432 pages
File Size : 54,8 Mb
Release : 2003
Category : Subject headings, Library of Congress
ISBN : OSU:32435070490032

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Library of Congress Subject Headings by Library of Congress Pdf

Author : S. Peszat,J. Zabczyk
Publisher : Cambridge University Press
Page : 45 pages
File Size : 48,5 Mb
Release : 2007-10-11
Category : Mathematics
ISBN : 9780521879897

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Stochastic Partial Differential Equations with Lévy Noise by S. Peszat,J. Zabczyk Pdf

Comprehensive monograph by two leading international experts; includes applications to statistical and fluid mechanics and to finance.

Author : H.J. Seifert,C.J.S. Clarke,A. Rosenblum
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400964464

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Mathematical Aspects of Superspace by H.J. Seifert,C.J.S. Clarke,A. Rosenblum Pdf

Over the past five years, through a continually increasing wave of activity in the physics community, supergravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the spectrum of elementary particles. Concurrently im portant mathematical works on the arena of supergravity has taken place, starting with Kostant's theory of graded manifolds and continuing with Batchelor's work linking this with the superspace formalism. There remains, however, a gap between the mathematical and physical approaches expressed by such unanswered questions as, does there exist a superspace having all the properties that physicists require of it? Does it make sense to perform path integral in such a space? It is hoped that these proceedings will begin a dialogue between mathematicians and physicists on such questions as the plan of renormalisation in supergravity. The contributors to the proceedings consist both of mathe maticians and relativists who bring their experience in differen tial geometry, classical gravitation and algebra and also quantum field theorists specialized in supersymmetry and supergravity. One of the most important problems associated with super symmetry is its relationship to the elementary particle spectrum.

Author : Yaozhong Hu
Publisher : World Scientific
Page : 484 pages
File Size : 54,5 Mb
Release : 2016-08-30
Category : Mathematics
ISBN : 9789813142190

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Analysis on Gaussian Spaces by Yaozhong Hu Pdf

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.