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The 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.           .

Mathematics. --- Random fields. --- Spectral theory (Mathematics). --- Stochastic control theory. --- Random fields --- Probabilities --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Probabilities. --- Mathematical physics. --- Cosmology. --- Probability Theory and Stochastic Processes. --- Mathematical Applications in the Physical Sciences. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Fields, Random --- Stochastic processes --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Astronomy --- Deism --- Metaphysics --- Physical mathematics --- Physics