Explicit extrapolation formulas for correlation models of homogeneous isotropic random fields
Authors:
N. V. Semenovs’ka and M. I. Yadrenko
Translated by:
V. Semenov
Journal:
Theor. Probability and Math. Statist. 69 (2004), 175-185
MSC (2000):
Primary 60J60, 60J12, 60J25
DOI:
https://doi.org/10.1090/S0094-9000-05-00624-1
Published electronically:
February 9, 2005
MathSciNet review:
2110915
Full-text PDF Free Access
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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
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- Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger, and Francesco G. Tricomi, Higher transcendental functions. Vols. I, II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. Based, in part, on notes left by Harry Bateman. MR 0058756
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References
- M. I. Yadrenko, Spectral Theory of Random Fields, “Vyshcha Shkola”, Kiev, 1980; English transl., Optimization Software, Inc., New York, 1983. MR 0590889 (82e:60001)
- A. M. Yaglom, Some classes of random fields in $n$-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)
- C. E. Buell, Correlation functions for wind and geopotential on isobaric surfaces, J. Appl. Meteor. 11 (1972), 51–59.
- I. S. Gradshteĭn 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)
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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)
- 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
Keywords:
Random fields,
Whittle–Mattern correlation model,
linear extrapolation
Received by editor(s):
February 14, 2003
Published electronically:
February 9, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
