A problem of minimax smoothing for homogeneous isotropic on a sphere random fields

A problem of minimax smoothing for homogeneous isotropic on a sphere random fields Random Oper. & Slocli. £<///., Vol. 1, No. 2, pp. 193-203 (1993) © VSP 1993 M. P. MOKLYACHUK Department of Mechanics and Mathematics, Kyjiv University, Kyjiv, 252017, Ukraine Received for ROSE 2 December 1991 Abstract--The problem of the least in a square-mean linear estimation for the transformation = «0>)i(-J>)TM»(d«) J=0 >/S of a homogeneous isotropic on a sphere 5n random field £(.;", x), j G N, x G Sn, using observations of i » ® ) + *?(.?> x ) f°r J ^ , 6 Sn, where (> x) is a homogeneous isotropic on a sphere Sn random field uncorrelated with £(*,z), is considered. The least favourable spectral densities and the minimax (robust) spectral characteristics are determined for some classes of spectral densities. 1. Let Sn be the unit sphere in the n- dimensional Euclidean space, m n ( · ) be the Lebesgue measure on Sn, Slm(x), xeSn, m = 0,1,..., / = l,2,...,fc(m,n), be the orthonormal spherical harmonics of degree ra, /i(m, n) = (2m + n - 2)(m + n - 3)!((n - 2)!m!)~1 being the number of linearly independent spherical harmonics of degree m (for properties of spherical harmonics, see [1-3]). Let £(j, x) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Random Operators and Stochastic Equations de Gruyter

A problem of minimax smoothing for homogeneous isotropic on a sphere random fields

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0926-6364
eISSN
1569-397X
DOI
10.1515/rose.1993.1.2.193
Publisher site
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Abstract

Random Oper. & Slocli. £<///., Vol. 1, No. 2, pp. 193-203 (1993) © VSP 1993 M. P. MOKLYACHUK Department of Mechanics and Mathematics, Kyjiv University, Kyjiv, 252017, Ukraine Received for ROSE 2 December 1991 Abstract--The problem of the least in a square-mean linear estimation for the transformation = «0>)i(-J>)TM»(d«) J=0 >/S of a homogeneous isotropic on a sphere 5n random field £(.;", x), j G N, x G Sn, using observations of i » ® ) + *?(.?> x ) f°r J ^ , 6 Sn, where (> x) is a homogeneous isotropic on a sphere Sn random field uncorrelated with £(*,z), is considered. The least favourable spectral densities and the minimax (robust) spectral characteristics are determined for some classes of spectral densities. 1. Let Sn be the unit sphere in the n- dimensional Euclidean space, m n ( · ) be the Lebesgue measure on Sn, Slm(x), xeSn, m = 0,1,..., / = l,2,...,fc(m,n), be the orthonormal spherical harmonics of degree ra, /i(m, n) = (2m + n - 2)(m + n - 3)!((n - 2)!m!)~1 being the number of linearly independent spherical harmonics of degree m (for properties of spherical harmonics, see [1-3]). Let £(j, x)

Journal

Random Operators and Stochastic Equationsde Gruyter

Published: Jan 1, 1993

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