Invariant Random Fields on Spaces with a Group Action

This book unifies much research scattered in the literature, and introduces new results first proved by the author. Also presents practical applications, in such highly interesting areas as approximation theory, cosmology and earthquake engineering.

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.

Highly interdisciplinary nature Fills a gap in the literature Many new results, and practical applications as for example in cosmology and earthquake engineering? Includes supplementary material: sn.pub/extras

Inhalt
1.Introduction.- 2.Spectral Expansions.- 3.L2 Theory of Invariant Random Fields.- 4.Sample Path Properties of Gaussian Invariant Random Fields.- 5.Applications.- A.Mathematical Background.- References.- Index.