A Theoretical Study of Estimation of Spherical Random Fields
Author: Johanna Frieda Stoeckler
Publisher:
Published: 1999
Total Pages: 184
ISBN-13:
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Author: Johanna Frieda Stoeckler
Publisher:
Published: 1999
Total Pages: 184
ISBN-13:
DOWNLOAD EBOOKAuthor: Domenico Marinucci
Publisher: Cambridge University Press
Published: 2011-08-25
Total Pages: 354
ISBN-13: 1139499823
DOWNLOAD EBOOKThe 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.
Author: Alexander G. Ramm
Publisher: World Scientific
Published: 2005
Total Pages: 390
ISBN-13: 9812565361
DOWNLOAD EBOOKThis book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory.This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory.
Author: Anatoliy Malyarenko
Publisher: Springer Science & Business Media
Published: 2012-10-26
Total Pages: 271
ISBN-13: 3642334067
DOWNLOAD EBOOKThe author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis, and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as it introduces new results from this area first proved by the author. The book also presents many practical applications, in particular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochastic processes, statistics, functional analysis, astronomy, and engineering.
Author: Alexander G. Ramm
Publisher: Longman Scientific and Technical
Published: 1990
Total Pages: 296
ISBN-13:
DOWNLOAD EBOOKAuthor: Alexander G. Ramm
Publisher:
Published: 1990
Total Pages: 282
ISBN-13: 9780608052397
DOWNLOAD EBOOKAuthor:
Publisher:
Published: 2002
Total Pages: 734
ISBN-13:
DOWNLOAD EBOOKAuthor: Erik Vanmarcke
Publisher: World Scientific
Published: 2010
Total Pages: 363
ISBN-13: 9812563539
DOWNLOAD EBOOKRandom 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.?
Author: Nicolai Leonenko
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 410
ISBN-13: 9401146071
DOWNLOAD EBOOKThis 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.
Author: Aleksandr Vadimovich Bulinski?
Publisher: World Scientific
Published: 2007
Total Pages: 447
ISBN-13: 9812709401
DOWNLOAD EBOOKThis 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.).