Random Fields: Analysis and Synthesis

Random variation over space and time is one of the few attributes that might safely be predicted as characterizing almost any given complex system. Random fields or "distributed disorder systems" confront astronomers, physicists, geologists, meteorologists, biologists, and other natural scientists. They appear in the artifacts developed by electrical, mechanical, civil, and other engineers. They even underlie the processes of social and economic change. The purpose of this book is to bring together existing and new methodologies of random field theory and indicate how they can be applied to these diverse areas where a "deterministic treatment is inefficient and conventional statistics insufficient." Many new results and methods are included.

After outlining the extent and characteristics of the random field approach, the book reviews the classical theory of multidimensional random processes and introduces basic probability concepts and methods in the random field context. It next gives a concise amount of the second-order analysis of homogeneous random fields, in both the space-time domain and the wave number-frequency domain. This is followed by a chapter on spectral moments and related measures of disorder and on level excursions and extremes of Gaussian and related random fields.

After developing a new framework of analysis based on local averages of one-, two-, and n-dimensional processes, the book concludes with a chapter discussing ramifications in the important areas of estimation, prediction, and control. The mathematical prerequisite has been held to basic college-level calculus.

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."