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

DOI:
https://doi.org/10.1090/S0094-9000-2011-00833-2

Published electronically:
August 5, 2011

MathSciNet review:
2790489

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Abstract | References | Similar Articles | Additional Information

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.

**1.**M. Ĭ. Jadrenko,*\cyr Spektral′naya teoriya sluchaĭnykh poleĭ*, “Vishcha Shkola”, Kiev, 1980 (Russian). MR**590889****2.**Yu. D. Popov,*Some problems of linear extrapolation for homogeneous, space isotropic, and time stationary random fields*, Dopovidi Akad. Nauk Ukrain. RSR Ser. A (1968), no. 12, 166-177. (Russian)**3.**M. V. Kartashov,*Finite-dimensional interpolation of a random field on the plane*, Teor. Ĭmovīr. Mat. Stat.**51**(1994), 53–61 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist.**51**(1995), 53–61 (1996). MR**1445052****4.**N. Semenovs′ka,*A problem of the interpolation of a homogeneous and isotropic random field*, Teor. Ĭmovīr. Mat. Stat.**74**(2006), 150–158 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist.**74**(2007), 171–179. MR**2336787**, https://doi.org/10.1090/S0094-9000-07-00706-5

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Additional Information

**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

DOI:
https://doi.org/10.1090/S0094-9000-2011-00833-2

Keywords:
Isotropic random field,
interpolation,
optimal estimates

Received by editor(s):
January 18, 2010

Published electronically:
August 5, 2011

Article copyright:
© Copyright 2011
American Mathematical Society