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.
Random Fields And Geometry
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Author : R. J. Adler
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-01-29
Random Fields And Geometry written by R. J. Adler 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 2009-01-29 with Mathematics categories.
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.
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.
Much of this book is concerned with autoregressive and moving av erage linear stationary sequences and random fields. These models are part of the classical literature in time series analysis, particularly in the Gaussian case. There is a large literature on probabilistic and statistical aspects of these models-to a great extent in the Gaussian context. In the Gaussian case best predictors are linear and there is an extensive study of the asymptotics of asymptotically optimal esti mators. Some discussion of these classical results is given to provide a contrast with what may occur in the non-Gaussian case. There the prediction problem may be nonlinear and problems of estima tion can have a certain complexity due to the richer structure that non-Gaussian models may have. Gaussian stationary sequences have a reversible probability struc ture, that is, the probability structure with time increasing in the usual manner is the same as that with time reversed. Chapter 1 considers the question of reversibility for linear stationary sequences and gives necessary and sufficient conditions for the reversibility. A neat result of Breidt and Davis on reversibility is presented. A sim ple but elegant result of Cheng is also given that specifies conditions for the identifiability of the filter coefficients that specify a linear non-Gaussian random field.
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.
Extreme Values In Random Sequences
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Author : Pavle Mladenović
language : en
Publisher: Springer Nature
Release Date : 2024-05-17
Extreme Values In Random Sequences written by Pavle Mladenović and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-17 with Mathematics categories.
The main subject is the probabilistic extreme value theory. The purpose is to present recent results related to limiting distributions of maxima in incomplete samples from stationary sequences, and results related to extremal properties of different combinatorial configurations. The necessary contents related to regularly varying functions and basic results of extreme value theory are included in the first two chapters with examples, exercises and supplements. The motivation for consideration maxima in incomplete samples arises from the fact that real data are often incomplete. A sequence of observed random variables from a stationary sequence is also stationary only in very special cases. Hence, the results provided in the third chapter are also related to non-stationary sequences. The proof of theorems related to joint limiting distribution of maxima in complete and incomplete samples requires a non-trivial combination of combinatorics and point process theory. Chapter four provides results on the asymptotic behavior of the extremal characteristics of random permutations, the coupon collector's problem, the polynomial scheme, random trees and random forests, random partitions of finite sets, and the geometric properties of samples of random vectors. The topics presented here provide insight into the natural connections between probability theory and algebra, combinatorics, graph theory and combinatorial geometry. The contents of the book may be useful for graduate students and researchers who are interested in probabilistic extreme value theory and its applications.
Statistical Analysis Of Random Fields
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Author : A. V. Ivanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Statistical Analysis Of Random Fields written by A. V. Ivanov 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.
Stationary Stochastic Processes
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Author : Georg Lindgren
language : en
Publisher: CRC Press
Release Date : 2012-10-01
Stationary Stochastic Processes written by Georg Lindgren and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-01 with Mathematics categories.
Intended for a second course in stationary processes, Stationary Stochastic Processes: Theory and Applications presents the theory behind the field’s widely scattered applications in engineering and science. In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes. Features Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields Explains how the basic theory is used in special applications like detection theory and signal processing, spatial statistics, and reliability Motivates mathematical theory from a statistical model-building viewpoint Introduces a selection of special topics, including extreme value theory, filter theory, long-range dependence, and point processes Provides more than 100 exercises with hints to solutions and selected full solutions This book covers key topics such as ergodicity, crossing problems, and extremes, and opens the doors to a selection of special topics, like extreme value theory, filter theory, long-range dependence, and point processes, and includes many exercises and examples to illustrate the theory. Precise in mathematical details without being pedantic, Stationary Stochastic Processes: Theory and Applications is for the student with some experience with stochastic processes and a desire for deeper understanding without getting bogged down in abstract mathematics.
Numerical Modelling Of Random Processes And Fields
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Author : Vitaliĭ Antonovich Ogorodnikov
language : en
Publisher: VSP
Release Date : 1996
Numerical Modelling Of Random Processes And Fields written by Vitaliĭ Antonovich Ogorodnikov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Computer-aided modelling is one of the most effective means of getting to the root of a natural phenomenon and of predicting the consequences of human impact on the environment. General methods of numerical modelling of random processes have been effectively developed and the area of applications has rapidly expanded in recent years. This book deals with the development and investigation of numerical methods for simulation of random processes and fields. The book opens with a description of scalar and vector-valued Gaussian models, followed by non-Gaussian models. Furthermore, issues of convergence of approximate models of random fields are studied. The last part of this book is devoted to applications of stochastic modelling, in which new application areas such as simulation of meteorological processes and fields, sea surface undulation, and stochastic structure of clouds, are presented.
Advances In Stochastic Inequalities
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Author : Theodore Preston Hill
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Advances In Stochastic Inequalities written by Theodore Preston Hill and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Contains 15 articles based on invited talks given at an AMS Special Session on 'Stochastic Inequalities and Their Applications' held at Georgia Institute of Technology (Atlanta). This book includes articles that offer a comprehensive picture of this area of mathematical probability and statistics.
Selected Works Of Murray Rosenblatt
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Author : Richard A. Davis
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-06
Selected Works Of Murray Rosenblatt written by Richard A. Davis 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 2011-05-06 with Mathematics categories.
During the second half of the 20th century, Murray Rosenblatt was one of the most celebrated and leading figures in probability and statistics. Among his many contributions, Rosenblatt conducted seminal work on density estimation, central limit theorems under strong mixing conditions, spectral domain methodology, long memory processes and Markov processes. He has published over 130 papers and 5 books, many as relevant today as when they first appeared decades ago. Murray Rosenblatt was one of the founding members of the Department of Mathematics at the University of California at San Diego (UCSD) and served as advisor to over twenty PhD students. He maintains a close association with UCSD in his role as Professor Emeritus. This volume is a celebration of Murray Rosenblatt's stellar research career that spans over six decades, and includes some of his most interesting and influential papers. Several leading experts provide commentary and reflections on various directions of Murray's research portfolio.