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Accuracy and reliability of a model for a Gaussian homogeneous and isotropic random field in the space $ L_p(\mathbb{T})$, $ p\geq 1$

Author: N. V. Troshki
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
Journal: Theor. Probability and Math. Statist. 90 (2015), 183-200
MSC (2010): Primary 60G15; Secondary 60G07
Published electronically: August 11, 2015
MathSciNet review: 3242030
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Abstract: A model is constructed for a Gaussian homogeneous isotropic random field that approximates it with a given accuracy and reliability in the space $ L_p(T)$, $ p\geq 1$. The theory of the spaces $ \operatorname {Sub}(\Omega )$ is used for studying such a model.

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Additional Information

N. V. Troshki
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine

Keywords: Gaussian random fields, homogeneous and isotropic fields, models of random fields, accuracy and reliability
Received by editor(s): March 11, 2014
Published electronically: August 11, 2015
Article copyright: © Copyright 2015 American Mathematical Society