Statistical modelling of a 3D random field by using the Kotelnikov–Shannon decomposition

Vyzhva, Z.; Fedorenko, K.

doi:10.1090/S0094-9000-2014-00916-3

Statistical modelling of a 3D random field by using the Kotelnikov–Shannon decomposition

Authors: Z. O. Vyzhva and K. V. Fedorenko
Translated by: S. Kvasko
Journal: Theor. Probability and Math. Statist. 88 (2014), 19-34
MSC (2010): Primary 60G60, 65C05
DOI: https://doi.org/10.1090/S0094-9000-2014-00916-3
Published electronically: July 24, 2014
MathSciNet review: 3112632
Full-text PDF Free Access

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Abstract: 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.

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