Statistical modelling of a 3D random field by using the Kotelnikov–Shannon decomposition
Zoya O. Vyzhva, K. Fedorenko · Theory of Probability and Mathematical Statistics · 2014
Real- valued random fields $\xi (t,x)$, $t \in \mathbf {R}$, $x \in \mathbf {R}^2$, that are homogeneous with respect to time and homogeneous isotropic with respect to spatial variables in the plane are studied. The problem of approximation of such random fields by random fields with a bounded spectrum is considered. An analogue of the Kotelnikov–Shannon theorem for random fields with a bounded spectrum is presented. Estimates of the mean-square approximation of random fields in the space $\mathbf {R}\times \mathbf {R}^2$ by a model constructed with the help of the spectral decomposition and interpolation Kotelnikov–Shannon formula are obtained. Some procedures for the statistical simulation of realizations of Gaussian random fields that are homogeneous with respect to time and homogeneous isotropic with respect to spatial variables in the plane are developed.