This 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.
Formulation of Basic Results Numerical Solution of the Basic Integral Equation in Distributions Proofs Singular Perturbation Theory for a Class of Fredholm Integral Equations Arising in Random Fields Estimation Theory Estimation and Scattering Theory Applications Auxiliary Results Appendices: Analytical Solution of the Basic Integral Equation for a Class of One-Dimensional Problems Integral Operators Basic in Random Fields Estimation Theory