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A problem of interpolation of a homogeneous and isotropic random field

Author(s): N. Semenovs'ka
Translated by: V. Zayats
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 74 (2006).
Journal: Theor. Probability and Math. Statist. No. 74 (2007), 171-179.
MSC (2000): Primary 60J60
Posted: July 5, 2007
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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 -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:

1.: M. V. Kartashov, Finite-dimensional interpolation of a random field on the sphere, Teor. Imovir. Mat. Stat. 51 (1995), 53-61; English transl. in Theory Probab. Math. Statist. 51 (1996), 53-61. MR 1445052 (97k:60142)
2.: M. I. Yadrenko, Spectral Theory of Random Fields, ``Vyshcha shkola'', Kiev, 1980; English transl., Optimization Software, New York, 1983. MR 697386 (84f:60003)
3.: 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

DOI: 10.1090/S0094-9000-07-00706-5
PII: S 0094-9000(07)00706-5
Keywords: Homogeneous and isotropic random fields, interpolation, approximation, limit of the error of approximation
Received by editor(s): 28/MAR/2005
Posted: July 5, 2007
Copyright of article: Copyright 2007, American Mathematical Society


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