Twenty Lectures About Gaussian Processes
Title | Twenty Lectures About Gaussian Processes PDF eBook |
Author | Vladimir Ilich Piterbarg |
Publisher | |
Pages | 182 |
Release | 2015-03-18 |
Genre | Mathematics |
ISBN | 9780984422197 |
"Twenty Lectures ..." is based on a course that Professor Piterbarg, a founder of the asymptotic theory of Gaussian processes and fields, teaches to higher-level undergraduate and graduate students at the Faculty of Mechanics and Mathematics, Lomonosov Moscow State University. Written in a clear and succinct style, the book provides a wide-ranging introduction to the field. The first half of the book is devoted to the general theory of Gaussian distributions in both finite- and infinite-dimensional vector spaces. Fundamental results, such as Slepian's, Fernique-Sudakov's and Berman's inequalities, among many others, are clearly explained from a modern, unified point of view. The second half of the book focuses on asymptotic methods, in particular on distributions of high extrema of Gaussian processes and fields. Foundational tools such as the Double Sum Method, the Method of Moments, and the Comparison Method, invented and popularized by the author, are prominently featured. This part adapts material from Professor Piterbarg's famous monograph to make it more accessible to a wider audience. No previous knowledge of stochastic processes is assumed, as all results are derived from a few basic facts of calculus and functional analysis. Written by a world-renowned expert in the field, "Twenty Lectures ..." is a must-read for students and experienced researchers alike - or anyone with an interest in Gaussian processes and fields. The text provides an excellent basis for a full-length graduate course. Albert N. Shiryaev, Member of the Russian Academy of Sciences, Chair of the Department of Probability Theory, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, says: "Professor Piterbarg's lectures are finally available in English and there is simply no other book on the subject that compares. Having contributed so much to the development of the asymptotic theory of Gaussian processes, the author manages to keep his lectures accessible yet rigorous. The lectures cover such a wide range of results and tools that this book is absolutely indispensable to anyone with an interest in the subject."
Lectures on Gaussian Processes
Title | Lectures on Gaussian Processes PDF eBook |
Author | Mikhail Lifshits |
Publisher | Springer Science & Business Media |
Pages | 129 |
Release | 2012-01-11 |
Genre | Mathematics |
ISBN | 3642249396 |
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.
Lectures on Gaussian Processes
Title | Lectures on Gaussian Processes PDF eBook |
Author | |
Publisher | |
Pages | 129 |
Release | 2012 |
Genre | |
ISBN |
An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes
Title | An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes PDF eBook |
Author | Robert J. Adler |
Publisher | IMS |
Pages | 198 |
Release | 1990 |
Genre | Mathematics |
ISBN | 9780940600171 |
Notes on Gaussian Processes
Title | Notes on Gaussian Processes PDF eBook |
Author | Naresh C. Jain |
Publisher | |
Pages | 110 |
Release | 1974* |
Genre | Gaussian processes |
ISBN |
Gaussian Processes, Function Theory, and the Inverse Spectral Problem
Title | Gaussian Processes, Function Theory, and the Inverse Spectral Problem PDF eBook |
Author | Harry Dym |
Publisher | Courier Corporation |
Pages | 354 |
Release | 2008-01-01 |
Genre | Mathematics |
ISBN | 048646279X |
This text offers background in function theory, Hardy functions, and probability as preparation for surveys of Gaussian processes, strings and spectral functions, and strings and spaces of integral functions. It addresses the relationship between the past and the future of a real, one-dimensional, stationary Gaussian process. 1976 edition.
An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes
Title | An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes PDF eBook |
Author | Robert J. Adler |
Publisher | |
Pages | 160 |
Release | 2008* |
Genre | Gaussian processes |
ISBN |
This e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press.