Strong Limit Theorems For Random Fields

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Limit Theorems For Associated Random Fields And Related Systems

Author : Alexander Bulinski
Publisher : World Scientific
ISBN 13 : 9814474576
Total Pages : 447 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Limit Theorems For Associated Random Fields And Related Systems by : Alexander Bulinski

Download or read book Limit Theorems For Associated Random Fields And Related Systems written by Alexander Bulinski and published by World Scientific. This book was released on 2007-09-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications.There are 434 items in the bibliography.The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).

Strong Limit Theorems for Random Fields

Author :
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (941 download)

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Book Synopsis Strong Limit Theorems for Random Fields by :

Download or read book Strong Limit Theorems for Random Fields written by and published by . This book was released on 2011 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Strong Limit Theorems for Quasi-orthogonal Random Fields

Author :
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (99 download)

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Book Synopsis Strong Limit Theorems for Quasi-orthogonal Random Fields by :

Download or read book Strong Limit Theorems for Quasi-orthogonal Random Fields written by and published by . This book was released on 1989 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Limit Theorems for Random Fields with Singular Spectrum

Author : Nikolai Leonenko
Publisher : Springer
ISBN 13 : 9789401146081
Total Pages : 406 pages
Book Rating : 4.1/5 (46 download)

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Book Synopsis Limit Theorems for Random Fields with Singular Spectrum by : Nikolai Leonenko

Download or read book Limit Theorems for Random Fields with Singular Spectrum written by Nikolai Leonenko and published by Springer. This book was released on 2011-09-29 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Limit Theorems for Random Fields with Singular Spectrum

Author : Nicolai Leonenko
Publisher : Springer Science & Business Media
ISBN 13 : 9401146071
Total Pages : 410 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Limit Theorems for Random Fields with Singular Spectrum by : Nicolai Leonenko

Download or read book Limit Theorems for Random Fields with Singular Spectrum written by Nicolai Leonenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents limit theorems for nonlinear functionals of random fields with singular spectrum on the basis of various asymptotic expansions. The first chapter treats basic concepts of the spectral theory of random fields, some important examples of random processes and fields with singular spectrum, and Tauberian and Abelian theorems for covariance function of long-memory random fields. Chapter 2 is devoted to limit theorems for spherical averages of nonlinear transformations of Gaussian and chi-square random fields. Chapter 3 summarises some limit theorems for geometric type functionals of random fields. Limit theorems for the solutions of Burgers' equation with random data via parabolic and hyperbolic rescaling are demonstrated in Chapter 4. Lastly, Chapter 5 deals with some problems for statistical analysis of random fields with singular spectrum. Audience: This book will be of interest to mathematicians who use random fields in engineering or other applications.

Strong Limit Theorems

Author : Lin Zhengyan
Publisher : Springer Science & Business Media
ISBN 13 : 9401730970
Total Pages : 204 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Strong Limit Theorems by : Lin Zhengyan

Download or read book Strong Limit Theorems written by Lin Zhengyan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an up-to-date review of the most significant developments in strong Approximation and strong convergence in probability theory. The book consists of three chapters. The first deals with Wiener and Gaussian processes. Chapter 2 is devoted to the increments of partial sums of independent random variables. Chapter 3 concentrates on the strong laws of processes generated by infinite-dimensional Ornstein-Uhlenbeck processes. For researchers whose work involves probability theory and statistics.

Limit theorems for random fields

Author : Nguyen Van Thu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (476 download)

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Book Synopsis Limit theorems for random fields by : Nguyen Van Thu

Download or read book Limit theorems for random fields written by Nguyen Van Thu and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Limit Theorems for Associated Random Fields and Related Systems

Author : Aleksandr Vadimovich Bulinskii
Publisher : World Scientific
ISBN 13 : 981270941X
Total Pages : 447 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Limit Theorems for Associated Random Fields and Related Systems by : Aleksandr Vadimovich Bulinskii

Download or read book Limit Theorems for Associated Random Fields and Related Systems written by Aleksandr Vadimovich Bulinskii and published by World Scientific. This book was released on 2007 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications. There are 434 items in the bibliography. The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.). Contents: Random Systems with Covariance Inequalities; Moment and Maximal Inequalities; Central Limit Theorem; Almost Sure Convergence; Invariance Principles; Law of the Iterated Logarithm; Statistical Applications; Integral Functionals. Readership: Researchers in modern probability and statistics, graduate students and academic staff of the universities.

Stationary Sequences and Random Fields

Author : Murray Rosenblatt
Publisher : Springer Science & Business Media
ISBN 13 : 1461251567
Total Pages : 253 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stationary Sequences and Random Fields by : Murray Rosenblatt

Download or read book Stationary Sequences and Random Fields written by Murray Rosenblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Geometry, Spatial Statistics and Random Fields

Author : Evgeny Spodarev
Publisher : Springer
ISBN 13 : 3642333052
Total Pages : 470 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Stochastic Geometry, Spatial Statistics and Random Fields by : Evgeny Spodarev

Download or read book Stochastic Geometry, Spatial Statistics and Random Fields written by Evgeny Spodarev and published by Springer. This book was released on 2013-02-11 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

Strong Limit Theorems in Non-Commutative Probability

Author : R. Jajte
Publisher : Springer
ISBN 13 : 3540391398
Total Pages : 159 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Strong Limit Theorems in Non-Commutative Probability by : R. Jajte

Download or read book Strong Limit Theorems in Non-Commutative Probability written by R. Jajte and published by Springer. This book was released on 2007-01-05 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Random Fields on the Sphere

Author : Domenico Marinucci
Publisher : Cambridge University Press
ISBN 13 : 1139499823
Total Pages : 354 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Random Fields on the Sphere by : Domenico Marinucci

Download or read book Random Fields on the Sphere written by Domenico Marinucci and published by Cambridge University Press. This book was released on 2011-08-25 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a comprehensive analysis of isotropic spherical random fields, with a view towards applications in cosmology. Any mathematician or statistician interested in these applications, especially the booming area of cosmic microwave background (CMB) radiation data analysis, will find the mathematical foundation they need in this book.

Limit Theorems for Multi-Indexed Sums of Random Variables

Author : Oleg Klesov
Publisher : Springer
ISBN 13 : 3662443880
Total Pages : 495 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Limit Theorems for Multi-Indexed Sums of Random Variables by : Oleg Klesov

Download or read book Limit Theorems for Multi-Indexed Sums of Random Variables written by Oleg Klesov and published by Springer. This book was released on 2014-10-13 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who work on limit theorems in probability theory, the statistical analysis of random fields, as well as in the field of random sets or stochastic geometry. The central topic is also important for statistical theory, developing statistical inferences for random fields, and also has applications to the sciences, including physics and chemistry.

Universal Theory For Strong Limit Theorems Of Probability

Author : Andrei N Frolov
Publisher : World Scientific
ISBN 13 : 9811212848
Total Pages : 204 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Universal Theory For Strong Limit Theorems Of Probability by : Andrei N Frolov

Download or read book Universal Theory For Strong Limit Theorems Of Probability written by Andrei N Frolov and published by World Scientific. This book was released on 2019-10-10 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book which the universal approach to strong laws of probability is discussed in. The universal theories are described for three important objects of probability theory: sums of independent random variables, processes with independent increments and renewal processes. Further generalizations are mentioned. Besides strong laws, large deviations are of independent interest. The case of infinite variations is considered as well. Readers can examine appropriate techniques and methods. Optimality of conditions is discussed.

Limit Theorems and Some Applications in Statistical Physics

Author : Boris Nahapetian
Publisher : Springer
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Limit Theorems and Some Applications in Statistical Physics by : Boris Nahapetian

Download or read book Limit Theorems and Some Applications in Statistical Physics written by Boris Nahapetian and published by Springer. This book was released on 1991-08 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Limit Theorems for Infinitely Divisible Random Fields

Author : Aurel Kleinerman
Publisher :
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Limit Theorems for Infinitely Divisible Random Fields by : Aurel Kleinerman

Download or read book Limit Theorems for Infinitely Divisible Random Fields written by Aurel Kleinerman and published by . This book was released on 1977 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables

Author : Shoumei Li
Publisher : Springer Science & Business Media
ISBN 13 : 9401599327
Total Pages : 399 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables by : Shoumei Li

Download or read book Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables written by Shoumei Li and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975). It is well known that the theory of set-valued random variables is a natural extension of that of general real-valued random variables or random vectors. However, owing to the topological structure of the space of closed sets and special features of set-theoretic operations ( cf. Beer [27]), set-valued random variables have many special properties. This gives new meanings for the classical probability theory. As a result of the development in this area in the past more than 30 years, the theory of set-valued random variables with many applications has become one of new and active branches in probability theory. In practice also, we are often faced with random experiments whose outcomes are not numbers but are expressed in inexact linguistic terms.