Abstract

The theory of random fields (random functions of several variables) continues to attract new applications such as turbulence theory, meteorology, statistical physics, and economics. We present some theoretical results for estimation of homogeneous and isotropic random fields with continuous parameters and weak or strong dependence (random fields with long memory). We consider the theory of estimation of regression coefficients of random fields observed on subsets of n dimensional Euclidean space (parallelepipeds, balls, spheres) and theory of estimation of correlation functions, including confidence intervals. We also consider the statistical model for parabolically rescaled Burgers equation with weakly or strongly dependent random initial conditions. This is joint work with Professor W. A. Woyczynski.

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