Interpolation of a homogeneous, space-isotropic, and time-stationary random field from observations on an infinite cylindrical surface. I
Author:N. Semenovs’ka Translated by:Oleg Klesov Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
Journal:
Theor. Probability and Math. Statist. 82 (2011), 139-148
MSC (2010):
Primary 60G60
Published electronically:
August 5, 2011
MathSciNet review:2790489 Full-text PDF
Abstract: We solve the problem of interpolation of a homogeneous, space-isotropic, and time-stationary random field in the case of a finite sample observed on an infinite cylindrical surface. An explicit formula for the corresponding mean square error of interpolation is obtained. The asymptotic behavior of the error is studied as the number of observations is increasing. Conditions for the error-free approximation are given. For the problem of the error-free approximation, we find an optimal distribution of the weight coefficients in the interpolation formula.
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N. Semenovs’ka Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email:
semenovska@mail.ru