Prediction Of Random Processses
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Author |
: Bruce Hajek |
Publisher |
: Cambridge University Press |
Total Pages |
: 429 |
Release |
: 2015-03-12 |
ISBN-10 |
: 9781316241240 |
ISBN-13 |
: 1316241246 |
Rating |
: 4/5 (40 Downloads) |
Synopsis Random Processes for Engineers by : Bruce Hajek
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 |
: Frank B. Knight |
Publisher |
: |
Total Pages |
: 272 |
Release |
: 1992 |
ISBN-10 |
: UOM:39015055578481 |
ISBN-13 |
: |
Rating |
: 4/5 (81 Downloads) |
Synopsis Foundations of the Prediction Process by : Frank B. Knight
This book presents a unified treatment of the prediction process approach to continuous time stochastic processes. The underling idea is that there are two kinds of time: stationary physical time and the moving observer's time. By developing this theme, the author develops a theory of stochastic processes whereby two processes are considered which coexist on the same probability space. In this way, the observer' process is strongly Markovian. Consequently, any measurable stochastic process of a real parameter may be regarded as a homogeneous strong Markov process in an appropriate setting. This leads to a unifying principle for the representation of general processes in terms of martingales which facilitates the prediction of their properties. While the ideas are advanced, the methods are reasonable elementary and should be accessible to readers with basic knowledge of measure theory, functional analysis, stochastic integration, and probability on the level of the convergence theorem for positive super-martingales.
Author |
: Robert S. Liptser |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 409 |
Release |
: 2013-03-14 |
ISBN-10 |
: 9783662100288 |
ISBN-13 |
: 3662100282 |
Rating |
: 4/5 (88 Downloads) |
Synopsis Statistics of Random Processes II by : Robert S. Liptser
"Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering....These books...will become classics." --SIAM REVIEW
Author |
: Hisashi Kobayashi |
Publisher |
: Cambridge University Press |
Total Pages |
: 813 |
Release |
: 2011-12-15 |
ISBN-10 |
: 9781139502610 |
ISBN-13 |
: 1139502611 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Probability, Random Processes, and Statistical Analysis by : Hisashi Kobayashi
Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.
Author |
: Harry Furstenberg |
Publisher |
: Princeton University Press |
Total Pages |
: 300 |
Release |
: 2016-03-02 |
ISBN-10 |
: 9781400881604 |
ISBN-13 |
: 1400881609 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Stationary Processes and Prediction Theory. (AM-44), Volume 44 by : Harry Furstenberg
A classic treatment of stationary processes and prediction theory from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Author |
: Frank B. Knight |
Publisher |
: IMS |
Total Pages |
: 120 |
Release |
: 1981 |
ISBN-10 |
: 0940600005 |
ISBN-13 |
: 9780940600003 |
Rating |
: 4/5 (05 Downloads) |
Synopsis Essays on the Prediction Process by : Frank B. Knight
Author |
: I.A. Ibragimov |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 285 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461262756 |
ISBN-13 |
: 1461262755 |
Rating |
: 4/5 (56 Downloads) |
Synopsis Gaussian Random Processes by : I.A. Ibragimov
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 |
: Denis Bosq |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 181 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781468404890 |
ISBN-13 |
: 146840489X |
Rating |
: 4/5 (90 Downloads) |
Synopsis Nonparametric Statistics for Stochastic Processes by : Denis Bosq
This book provides a mathematically rigorous treatment of the theory of nonparametric estimation and prediction for stochastic processes. It discusses discrete time and continuous time, and the emphasis is on the kernel methods. Several new results are presented concerning optimal and superoptimal convergence rates. How to implement the method is discussed in detail and several numerical results are presented. This book will be of interest to specialists in mathematical statistics and to those who wish to apply these methods to practical problems involving time series analysis.
Author |
: Robert Shevilevich Lipt︠s︡er |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 428 |
Release |
: 2001 |
ISBN-10 |
: 3540639284 |
ISBN-13 |
: 9783540639282 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Statistics of Random Processes II by : Robert Shevilevich Lipt︠s︡er
"Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering....These books...will become classics." --SIAM REVIEW
Author |
: Robert Liptser |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 450 |
Release |
: 2001 |
ISBN-10 |
: 3540639292 |
ISBN-13 |
: 9783540639299 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Statistics of Random Processes by : Robert Liptser
These volumes cover non-linear filtering (prediction and smoothing) theory and its applications to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. Also presented is the theory of martingales, of interest to those who deal with problems in financial mathematics. These editions include new material, expanded chapters, and comments on recent progress in the field.