Gaussian Random Processes PDF Download
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Author | : I.A. Ibragimov |
Publisher | : Springer Science & Business Media |
Total Pages | : 285 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461262755 |
Download Gaussian Random Processes Book in PDF, ePub and Kindle
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.
Author | : Gennady Samoradnitsky |
Publisher | : Routledge |
Total Pages | : 632 |
Release | : 2017-11-22 |
Genre | : Mathematics |
ISBN | : 1351414801 |
Download Stable Non-Gaussian Random Processes Book in PDF, ePub and Kindle
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.
Author | : Carl Edward Rasmussen |
Publisher | : MIT Press |
Total Pages | : 266 |
Release | : 2005-11-23 |
Genre | : Computers |
ISBN | : 026218253X |
Download Gaussian Processes for Machine Learning Book in PDF, ePub and Kindle
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.
Author | : E. Wong |
Publisher | : Springer Science & Business Media |
Total Pages | : 183 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475717954 |
Download Introduction to Random Processes Book in PDF, ePub and Kindle
Author | : M.A. Lifshits |
Publisher | : Springer Science & Business Media |
Total Pages | : 347 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401584745 |
Download Gaussian Random Functions Book in PDF, ePub and Kindle
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 | : Vidyadhar S. Mandrekar |
Publisher | : CRC Press |
Total Pages | : 200 |
Release | : 2015-06-23 |
Genre | : Mathematics |
ISBN | : 1498707823 |
Download Stochastic Analysis for Gaussian Random Processes and Fields Book in PDF, ePub and Kindle
Stochastic Analysis for Gaussian Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it studies Gaussian random fields using reproducing kernel Hilbert spaces (RKHSs).The book begins with preliminary results on covariance and associated RKHS
Author | : Marvin K. Simon |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2007-05-24 |
Genre | : Mathematics |
ISBN | : 0387476946 |
Download Probability Distributions Involving Gaussian Random Variables Book in PDF, ePub and Kindle
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.
Author | : Mikhail Lifshits |
Publisher | : Springer Science & Business Media |
Total Pages | : 129 |
Release | : 2012-01-11 |
Genre | : Mathematics |
ISBN | : 3642249396 |
Download Lectures on Gaussian Processes Book in PDF, ePub and Kindle
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.
Author | : Bruce Hajek |
Publisher | : Cambridge University Press |
Total Pages | : 429 |
Release | : 2015-03-12 |
Genre | : Technology & Engineering |
ISBN | : 1316241246 |
Download Random Processes for Engineers Book in PDF, ePub and Kindle
This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).
Author | : Gennady Samoradnitsky |
Publisher | : Routledge |
Total Pages | : 662 |
Release | : 2017-11-22 |
Genre | : Mathematics |
ISBN | : 1351414798 |
Download Stable Non-Gaussian Random Processes Book in PDF, ePub and Kindle
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.