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

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **88** (2013).

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

Abstract | References | Similar Articles | Additional Information

Abstract: Real- valued random fields , , , 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 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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Additional Information

**Z. O. Vyzhva**

Affiliation:
Department of General Mathematics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue, 4-e, Kyiv 03127, Ukraine

Email:
vsa@univ.kiev.ua

**K. V. Fedorenko**

Affiliation:
Department of General Mathematics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue, 4-e, Kyiv 03127, Ukraine

Email:
slimsmentol@mail.ru

DOI:
https://doi.org/10.1090/S0094-9000-2014-00916-3

Keywords:
Random fields,
modelling,
Kotelnikov--Shannon decomposition

Received by editor(s):
February 13, 2012

Published electronically:
July 24, 2014

Article copyright:
© Copyright 2014
American Mathematical Society