Stochastic Spectral and Fourier-Wavelet Methods for Vector Gaussian Random Fields

Abstract

Randomized Spectral Models (RSM) and Randomized Fourier-Wavelet Models (FWM) for simulation of homogeneous Gaussian random fields based on spectral representations and plane wave decomposition of random fields are developed. Extensions of FWM to vector random processes are constructed. Convergence of the constructed Fourier-Wavelet models (in the sense of finite-dimensional distributions) under some general conditions on the spectral tensor is given. A comparative analysis of RSM and FWM is made by calculating Eulerian statistical characteristics of a 3D isotropic incompressible random field through an ensemble and space averaging.