Gaussian Random Processes

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Gaussian Random Processes

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Author : I.A. Ibragimov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Gaussian Random Processes written by I.A. Ibragimov 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 2012-12-06 with Mathematics categories.

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.

Gaussian Processes For Machine Learning

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Author : Carl Edward Rasmussen
language : en
Publisher: MIT Press
Release Date : 2005-11-23

Gaussian Processes For Machine Learning written by Carl Edward Rasmussen and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-23 with Computers categories.

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.

Stable Non Gaussian Random Processes

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Author : Gennady Samoradnitsky
language : en
Publisher: Routledge
Release Date : 2017-11-22

Stable Non Gaussian Random Processes written by Gennady Samoradnitsky and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.

This book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.

Lectures On Gaussian Processes

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Author : Mikhail Lifshits
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-11

Lectures On Gaussian Processes written by Mikhail Lifshits 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 2012-01-11 with Mathematics categories.

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.​

Gaussian Random Functions

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Author : M.A. Lifshits
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-02-28

Gaussian Random Functions written by M.A. Lifshits 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 1995-02-28 with Mathematics categories.

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

Random Processes For Engineers

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Author : Bruce Hajek
language : en
Publisher: Cambridge University Press
Release Date : 2015-03-12

Random Processes For Engineers written by Bruce Hajek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Computers categories.

An engaging introduction to the critical tools needed to design and evaluate engineering systems operating in uncertain environments.

Markov Processes Gaussian Processes And Local Times

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Author : Michael B. Marcus
language : en
Publisher: Cambridge University Press
Release Date : 2006-07-24

Markov Processes Gaussian Processes And Local Times written by Michael B. Marcus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-24 with Mathematics categories.

A readable 2006 synthesis of three main areas in the modern theory of stochastic processes.

Introduction To Probability Statistics And Random Processes

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Author : Hossein Pishro-Nik
language : en
Publisher:
Release Date : 2014-08-15

Introduction To Probability Statistics And Random Processes written by Hossein Pishro-Nik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-15 with Probabilities categories.

The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.

Probability Distributions Involving Gaussian Random Variables

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Author : Marvin K. Simon
language : en
Publisher: Springer
Release Date : 2006-11-09

Probability Distributions Involving Gaussian Random Variables written by Marvin K. Simon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-09 with Mathematics categories.

This handbook, now available in paperback, brings together a comprehensive collection of mathematical material in one location. It also offers a variety of new results interpreted in a form that is particularly useful to engineers, scientists, and applied mathematicians. The handbook is not specific to fixed research areas, but rather it has a generic flavor that can be applied by anyone working with probabilistic and stochastic analysis and modeling. Classic results are presented in their final form without derivation or discussion, allowing for much material to be condensed into one volume.