The Geometry of Random Fields PDF Download

Author: Robert J. Adler
Publisher: SIAM
ISBN: 0898716934
Category : Mathematics
Languages : en
Pages : 295

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Book Description
An important treatment of the geometric properties of sets generated by random fields, including a comprehensive treatment of the mathematical basics of random fields in general. It is a standard reference for all researchers with an interest in random fields, whether they be theoreticians or come from applied areas.

Author: R. J. Adler
Publisher: Springer Science & Business Media
ISBN: 0387481168
Category : Mathematics
Languages : en
Pages : 455

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Book Description
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.

Author: Robert J. Adler
Publisher:
ISBN: 9780817641542
Category : Mathematics
Languages : en
Pages : 456

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Book Description
This self-contained monograph contains a number of topics that focus on the many developments in the area of mathematical probability/statistics known as random fields. Robert Adler has been one of the major contributors to this subject. In an earlier work (1981) he dealt with a wide variety of geometrical problems that are unique to stochastic processes in dimensions higher than one, fashioning an interesting blend of geometry and probability. Some old classical topics (non-geometric in nature) are presented in the first few chapters, but the material has been recast in the post-1980 setting of entropy. This is followed by a treatment of random geometry which takes into account the recent work by Worsley et al, and a significant update on our understanding of the fractal nature of erratic random fields. The geometric theme of the book is carried throughout in a user- friendly style. As in his previous work, Adler engages scientists outside of pure and applied mathematics, in particular, researchers involved in brain imaging, and astrophysicists. Applications of excursion set theory in astrophysics and brain imaging are detailed in a short chapter.It is hope that the approach employed in these two quite different areas will direct the reader to finding applications elsewhere. In recent years, the geometry of random fields has also found its way into the literature of materials (surface) science, oceanography, and geology. For applications in the medical community, a chapter discussing the tube formula approach involves the geometry on manifolds and an examination of the distribution of the maximum of Gaussian random

Author: Evgeny Spodarev
Publisher: Springer
ISBN: 3642333052
Category : Mathematics
Languages : en
Pages : 470

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Book Description
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.

Author: George Christakos
Publisher: Elsevier
ISBN: 0128030321
Category : Science
Languages : en
Pages : 698

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Book Description
Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of spatiotemporal random field models to problems in ocean, earth, and atmospheric sciences, spatiotemporal statistics, and geostatistics, among others. The new edition features considerable detail of spatiotemporal random field theory, including ordinary and generalized models, as well as space-time homostationary, isostationary and hetrogeneous approaches. Presenting new theoretical and applied results, with particular emphasis on space-time determination and interpretation, spatiotemporal analysis and modeling, random field geometry, random functionals, probability law, and covariance construction techniques, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time variability functions, the validity of major theoretical assumptions in real-world practice (covariance positive-definiteness, metric-adequacy etc.), and the emergence of interdisciplinary phenomena in conditions of multi-sourced real-world uncertainty. Contains applications in the form of examples and case studies, providing readers with first-hand experiences Presents an easy to follow narrative which progresses from simple concepts to more challenging ideas Includes significant updates from the previous edition, including a focus on new theoretical and applied results

Author: Volker Schmidt
Publisher: Springer
ISBN: 3319100645
Category : Mathematics
Languages : en
Pages : 484

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Book Description
This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.

Author: Dionissios T. Hristopulos
Publisher: Springer Nature
ISBN: 9402419187
Category : Science
Languages : en
Pages : 884

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Book Description
This book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.

Author: Jean-Marc Azais
Publisher: John Wiley & Sons
ISBN: 0470434635
Category : Mathematics
Languages : en
Pages : 407

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Book Description
A timely and comprehensive treatment of random field theory with applications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses how to understand the properties of the level sets of paths as well as how to compute the probability distribution of its extremal values, which are two general classes of problems that arise in the study of random processes and fields and in related applications. This book provides a unified and accessible approach to these two topics and their relationship to classical theory and Gaussian processes and fields, and the most modern research findings are also discussed. The authors begin with an introduction to the basic concepts of stochastic processes, including a modern review of Gaussian fields and their classical inequalities. Subsequent chapters are devoted to Rice formulas, regularity properties, and recent results on the tails of the distribution of the maximum. Finally, applications of random fields to various areas of mathematics are provided, specifically to systems of random equations and condition numbers of random matrices. Throughout the book, applications are illustrated from various areas of study such as statistics, genomics, and oceanography while other results are relevant to econometrics, engineering, and mathematical physics. The presented material is reinforced by end-of-chapter exercises that range in varying degrees of difficulty. Most fundamental topics are addressed in the book, and an extensive, up-to-date bibliography directs readers to existing literature for further study. Level Sets and Extrema of Random Processes and Fields is an excellent book for courses on probability theory, spatial statistics, Gaussian fields, and probabilistic methods in real computation at the upper-undergraduate and graduate levels. It is also a valuable reference for professionals in mathematics and applied fields such as statistics, engineering, econometrics, mathematical physics, and biology.

Author: Erik Vanmarcke
Publisher: World Scientific
ISBN: 9812563539
Category : Mathematics
Languages : en
Pages : 363

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Book Description
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.?

Author: Anatoliy Malyarenko
Publisher: Cambridge University Press
ISBN: 1108429858
Category : Science
Languages : en
Pages : 313

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Book Description
Presents a complete description of homogenous and isotropic tensor-valued random fields, including the problems of continuum physics, mathematical tools and applications.