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Explicit extrapolation formulas for correlation models of homogeneous isotropic random fields
Author(s):
N.
V.
Semenovs'ka;
M.
I.
Yadrenko
Translated by:
V. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 69
(2003).
Journal:
Theor. Probability and Math. Statist.
No. 69
(2004),
175-185.
MSC (2000):
Primary 60J60, 60J12, 60J25
Posted:
February 9, 2005
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Additional information
Abstract:
For some correlation models of homogeneous isotropic random fields, we obtain explicit formulas for linear extrapolation of a random field to the center of a sphere from observations on the sphere.
References:
-
- 1.
- M. I. Yadrenko, Spectral Theory of Random Fields, ``Vyshcha Shkola'', Kiev, 1980; English transl., Optimization Software, Inc., New York, 1983. MR 0590889 (82e:60001)
- 2.
- A. M. Yaglom, Some classes of random fields in
 -dimensional space related to stationary random processes, Teor. Veroyatnost. i Primenen. 2 (1957), no. 3, 292-338; English transl. in Theory Probab. Appl. 2 (1957), no. 3, 273-320. MR 0094844 (20:1353) - 3.
- C. E. Buell, Correlation functions for wind and geopotential on isobaric surfaces, J. Appl. Meteor. 11 (1972), 51-59.
- 4.
- I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, and Products, Gos. Izdat. Fiz. Mat. Literat., Moscow, 1963; English transl., Sixth edition, Academic Press, San Diego, CA, 2000. MR 1773820 (2001c:00002)
- 5.
- M. I. Yadrenko, Some statistical problems for the Whittle random field, Teor. Imovir. Mat. Stat. 63 (2000), 163-167; English transl. in Theory Probab. Math. Statist. 63 (2001), 179-183. MR 1870787 (2002m:60097)
- 6.
- G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd edition, Cambridge University Press, Cambridge, 1995. MR 1349110 (96i:33010)
- 7.
- A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, Based in part on notes left by Harry Bateman, vol. 1, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. MR 0058756 (15:419i)
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- -, Higher Transcendental Functions, Based in part on notes left by Harry Bateman, vol. 2, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. MR 0058756 (15:419i)
- 9.
- M. I. Yadrenko, Isotropic random fields of Markov type in Euclidean and Hilbert spaces, Proc. All-Union Conf. Theory Prob. and Math. Statist. (Erevan, 1958), Izdat. Akad. Nauk Armyan. SSR, Erevan, 1960, pp. 263-279. (Russian) MR 0214123 (35:4974)
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Additional Information:
N.
V.
Semenovs'ka
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
semenovsky@hotmail.ru
M.
I.
Yadrenko
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
ymi@mechmat.univ.kiev.ua
DOI:
10.1090/S0094-9000-05-00624-1
PII:
S 0094-9000(05)00624-1
Keywords:
Random fields,
Whittle--Mattern correlation model,
linear extrapolation
Received by editor(s):
14/FEB/2003
Posted:
February 9, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
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