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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
Published electronically: July 24, 2014
MathSciNet review: 3112632
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Abstract | References | Similar Articles | Additional Information

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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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