A problem of interpolation of a homogeneous and isotropic random field
Author:
N. Semenovs’ka
Translated by:
V. Zayats
Journal:
Theor. Probability and Math. Statist. 74 (2007), 171-179
MSC (2000):
Primary 60J60
DOI:
https://doi.org/10.1090/S0094-9000-07-00706-5
Published electronically:
July 5, 2007
MathSciNet review:
2336787
Full-text PDF Free Access
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Abstract: A solution to the interpolation problem for the value of a homogeneous and isotropic random field at an arbitrary point inside an $n$-dimensional sphere after observations on a finite set of points on the sphere is found. The asymptotic behavior of the interpolation error as the number of points increases is studied. Recommendations on where the observation points should be placed on the sphere are given.
References
- 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
- M. Ĭ. Yadrenko, Spectral theory of random fields, Translation Series in Mathematics and Engineering, Optimization Software, Inc., Publications Division, New York, 1983. Translated from the Russian. MR 697386
- N. N. Lebedev, Special functions and their applications, Dover Publications, Inc., New York, 1972. Revised edition, translated from the Russian and edited by Richard A. Silverman; Unabridged and corrected republication. MR 0350075
References
- M. V. Kartashov, Finite-dimensional interpolation of a random field on the sphere, Teor. Ĭmovīr. Mat. Stat. 51 (1995), 53–61; English transl. in Theory Probab. Math. Statist. 51 (1996), 53–61. MR 1445052 (97k:60142)
- M. I. Yadrenko, Spectral Theory of Random Fields, “Vyshcha shkola”, Kiev, 1980; English transl., Optimization Software, New York, 1983. MR 697386 (84f:60003)
- N. N. Lebedev, Special Functions and Their Applications, “Nauka”, Moscow, 1963; English transl., Dover Publications, Inc., New York, 1972. MR 0350075 (50:2568)
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Additional Information
N. Semenovs’ka
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01033, Ukraine
Email:
semenovsky@voliacable.com
Keywords:
Homogeneous and isotropic random fields,
interpolation,
approximation,
limit of the error of approximation
Received by editor(s):
March 28, 2005
Published electronically:
July 5, 2007
Article copyright:
© Copyright 2007
American Mathematical Society
