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Infinite Dimensional Gaussian Distributions
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Book Synopsis Infinite-Dimensional Gaussian Distributions by : I͡Uriĭ Anatolʹevich Rozanov
Download or read book Infinite-Dimensional Gaussian Distributions written by I͡Uriĭ Anatolʹevich Rozanov and published by American Mathematical Soc.. This book was released on 1971 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Infinite-dimensional Gaussian Distributions by : IU. A. (Iurii Anatol'evich) Rozanov
Download or read book Infinite-dimensional Gaussian Distributions written by IU. A. (Iurii Anatol'evich) Rozanov and published by . This book was released on 1971 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Gaussian Measures by : Vladimir I. Bogachev
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.
Book Synopsis Infinite-dimensional Gaussian distributions (Gaussovskie beskonečnomernye raspredelenija, engl.- Transl. from the Russ. by G. Biriuk) by : Jurij Anatol'evič Rozanov
Download or read book Infinite-dimensional Gaussian distributions (Gaussovskie beskonečnomernye raspredelenija, engl.- Transl. from the Russ. by G. Biriuk) written by Jurij Anatol'evič Rozanov and published by . This book was released on 1971 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Problems in the Theory of Infinite-dimensional Probability Distributions by : V. N. Sudakov
Download or read book Geometric Problems in the Theory of Infinite-dimensional Probability Distributions written by V. N. Sudakov and published by American Mathematical Soc.. This book was released on 1979 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses problems in the distribution theory of probability.
Book Synopsis Infinite-dimensional Gaussian Distribution by : Iurii Anatol'evich Rozanov
Download or read book Infinite-dimensional Gaussian Distribution written by Iurii Anatol'evich Rozanov and published by . This book was released on 1971 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Gaussian Random Functions by : M.A. Lifshits
Download or read book Gaussian Random Functions written by M.A. Lifshits and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Analysis On Gaussian Spaces by : Yaozhong Hu
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.
Book Synopsis Lectures on Gaussian Processes by : Mikhail Lifshits
Download or read book Lectures on Gaussian Processes written by Mikhail Lifshits and published by Springer Science & Business Media. This book was released on 2012-01-11 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.
Book Synopsis Gaussian Measures in Finite and Infinite Dimensions by : Daniel W. Stroock
Download or read book Gaussian Measures in Finite and Infinite Dimensions written by Daniel W. Stroock and published by Springer Nature. This book was released on 2023-02-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Gaussian Processes for Machine Learning by : Carl Edward Rasmussen
Download or read book Gaussian Processes for Machine Learning written by Carl Edward Rasmussen and published by MIT Press. This book was released on 2005-11-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
Book Synopsis High-Dimensional Probability by : Roman Vershynin
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Book Synopsis Gaussian Random Processes by : I.A. Ibragimov
Download or read book Gaussian Random Processes written by I.A. Ibragimov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.
Book Synopsis Sums and Gaussian Vectors by : Vadim Yurinsky
Download or read book Sums and Gaussian Vectors written by Vadim Yurinsky and published by Springer. This book was released on 2006-11-14 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces by : Kiyosi Ito
Download or read book Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces written by Kiyosi Ito and published by SIAM. This book was released on 1984-01-01 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces.
Book Synopsis Introduction to Hida Distributions by : Si Si
Download or read book Introduction to Hida Distributions written by Si Si and published by World Scientific. This book was released on 2012 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the mathematical definition of white noise and gives its significance. White noise is in fact a typical class of idealized elemental (infinitesimal) random variables. Thus, we are naturally led to have functionals of such elemental random variables that is white noise. This book analyzes those functionals of white noise, particularly the generalized ones called Hida distributions, and highlights some interesting future directions. The main part of the book involves infinite dimensional differential and integral calculus based on the variable which is white noise.The present book can be used as a supplementary book to Lectures on White Noise Functionals published in 2008, with detailed background provided.
Book Synopsis Gaussian Hilbert Spaces by : Svante Janson
Download or read book Gaussian Hilbert Spaces written by Svante Janson and published by Cambridge University Press. This book was released on 1997-06-12 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
