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Theory of Probability and Mathematical Statistics

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A problem of interpolation of a homogeneous and isotropic random field

Author: N. Semenovs'ka
Translated by: V. Zayats
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 74 (2006).
Journal: Theor. Probability and Math. Statist. 74 (2007), 171-179
MSC (2000): Primary 60J60
Published electronically: July 5, 2007
MathSciNet review: 2336787
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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 [Enhancements On Off] (What's this?)

  • 1. 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
  • 2. 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
  • 3. 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

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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

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

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