Stationary Sequences And Random Fields
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Stationary Sequences And Random Fields
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Author : Murray Rosenblatt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stationary Sequences And Random Fields written by Murray Rosenblatt 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.
This book has a dual purpose. One of these is to present material which selec tively will be appropriate for a quarter or semester course in time series analysis and which will cover both the finite parameter and spectral approach. The second object is the presentation of topics of current research interest and some open questions. I mention these now. In particular, there is a discussion in Chapter III of the types of limit theorems that will imply asymptotic nor mality for covariance estimates and smoothings of the periodogram. This dis cussion allows one to get results on the asymptotic distribution of finite para meter estimates that are broader than those usually given in the literature in Chapter IV. A derivation of the asymptotic distribution for spectral (second order) estimates is given under an assumption of strong mixing in Chapter V. A discussion of higher order cumulant spectra and their large sample properties under appropriate moment conditions follows in Chapter VI. Probability density, conditional probability density and regression estimates are considered in Chapter VII under conditions of short range dependence. Chapter VIII deals with a number of topics. At first estimates for the structure function of a large class of non-Gaussian linear processes are constructed. One can determine much more about this structure or transfer function in the non-Gaussian case than one can for Gaussian processes. In particular, one can determine almost all the phase information.
Gaussian And Non Gaussian Linear Time Series And Random Fields
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Author : Murray Rosenblatt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Gaussian And Non Gaussian Linear Time Series And Random Fields written by Murray Rosenblatt 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 principal focus here is on autoregressive moving average models and analogous random fields, with probabilistic and statistical questions also being discussed. The book contrasts Gaussian models with noncausal or noninvertible (nonminimum phase) non-Gaussian models and deals with problems of prediction and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. Intended as a text for gradutes in statistics, mathematics, engineering, the natural sciences and economics, the only recommendation is an initial background in probability theory and statistics. Notes on background, history and open problems are given at the end of the book.
An Introduction To The Theory Of Stationary Random Functions
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Author : A. M. Yaglom
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
An Introduction To The Theory Of Stationary Random Functions written by A. M. Yaglom and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
This two-part treatment covers the general theory of stationary random functions and the Wiener-Kolmogorov theory of extrapolation and interpolation of random sequences and processes. Beginning with the simplest concepts, it covers the correlation function, the ergodic theorem, homogenous random fields, and general rational spectral densities, among other topics. Numerous examples appear throughout the text, with emphasis on the physical meaning of mathematical concepts. Although rigorous in its treatment, this is essentially an introduction, and the sole prerequisites are a rudimentary knowledge of probability and complex variable theory. 1962 edition.
Measures Of Dependence On Stationary Sequences Of Random Variables
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Author : Richard Crane Bradley
language : en
Publisher:
Release Date : 1978
Measures Of Dependence On Stationary Sequences Of Random Variables written by Richard Crane Bradley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Random variables categories.
Correlation Theory Of Stationary And Related Random Functions
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Author : A.M. Yaglom
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Correlation Theory Of Stationary And Related Random Functions written by A.M. Yaglom 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.
Correlation Theory of Stationary and Related Random Functions is an elementary introduction to the most important part of the theory dealing only with the first and second moments of these functions. This theory is a significant part of modern probability theory and offers both intrinsic mathematical interest and many concrete and practical applications. Stationary random functions arise in connection with stationary time series which are so important in many areas of engineering and other applications. This book presents the theory in such a way that it can be understood by readers without specialized mathematical backgrounds, requiring only the knowledge of elementary calculus. The first volume in this two-volume exposition contains the main theory; the supplementary notes and references of the second volume consist of detailed discussions of more specialized questions, some more additional material (which assumes a more thorough mathematical background than the rest of the book) and numerous references to the extensive literature.
Iindependent And Stationary Sequences Of Random Variables
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Author : I. A.L. Ibragimov
language : en
Publisher:
Release Date :
Iindependent And Stationary Sequences Of Random Variables written by I. A.L. Ibragimov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Random Fields On A Network
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Author : Xavier Guyon
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-06-23
Random Fields On A Network written by Xavier Guyon 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 1995-06-23 with Mathematics categories.
The theory of spatial models over lattices, or random fields as they are known, has developed significantly over recent years. This book provides a graduate-level introduction to the subject which assumes only a basic knowledge of probability and statistics, finite Markov chains, and the spectral theory of second-order processes. A particular strength of this book is its emphasis on examples - both to motivate the theory which is being developed, and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms.
Independent And Stationary Sequences Of Random Variables
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Author : Ilʹdar Abdulovich Ibragimov
language : en
Publisher:
Release Date : 1971
Independent And Stationary Sequences Of Random Variables written by Ilʹdar Abdulovich Ibragimov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Distribution (Probability theory). categories.
Random Fields
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Author : Erik Vanmarcke
language : en
Publisher: World Scientific
Release Date : 2010
Random Fields written by Erik Vanmarcke and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Random variation is a fact of life that provides substance to a wide range of problems in the sciences, engineering, and economics. There is a growing need in diverse disciplines to model complex patterns of variation and interdependence using random fields, as both deterministic treatment and conventional statistics are often insufficient. An ideal random field model will capture key features of complex random phenomena in terms of a minimum number of physically meaningful and experimentally accessible parameters. This volume, a revised and expanded edition of an acclaimed book first published by the M I T Press, offers a synthesis of methods to describe and analyze and, where appropriate, predict and control random fields. There is much new material, covering both theory and applications, notably on a class of probability distributions derived from quantum mechanics, relevant to stochastic modeling in fields such as cosmology, biology and system reliability, and on discrete-unit or agent-based random processes.Random Fields is self-contained and unified in presentation. The first edition was found, in a review in EOS (American Geophysical Union) to be ?both technically interesting and a pleasure to read ? the presentation is clear and the book should be useful to almost anyone who uses random processes to solve problems in engineering or science ? and (there is) continued emphasis on describing the mathematics in physical terms.?
The Geometry Of Random Fields
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Author : Robert J. Adler
language : en
Publisher: SIAM
Release Date : 1981-01-01
The Geometry Of Random Fields written by Robert J. Adler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Mathematics categories.
Originally published in 1981, The Geometry of Random Fields remains an important text for its coverage and exposition of the theory of both smooth and nonsmooth random fields; closed form expressions for the various geometric characteristics of the excursion sets of smooth, stationary, Gaussian random fields over N-dimensional rectangles; descriptions of the local behavior of random fields in the neighborhoods of high maxima; and a treatment of the Markov property for Gaussian fields. Audience: researchers in probability and statistics, with no prior knowledge of geometry required. Since the book was originally published it has become a standard reference in areas of physical oceanography, cosmology, and neuroimaging. It is written at a level accessible to nonspecialists, including advanced undergraduates and early graduate students.