Estimation Problems for Periodically Correlated Isotropic Random Fields

Estimation Problems for Random Fields
  • Iryna Dubovetska
  • Oleksandr Masyutka
  • Mikhail MoklyachukEmail author


Spectral theory of isotropic random fields in Euclidean space developed by M. I. Yadrenko is exploited to find a solution to the problem of optimal linear estimation of the functional
$$ A\zeta ={\sum\limits_{t=0}^{\infty}}\,\,\,{\int_{S_n}} \,\,a(t,x)\zeta (t,x)\,m_n(dx) $$
which depends on unknown values of a periodically correlated (cyclostationary with period T) with respect to time isotropic on the sphere S n in Euclidean space E n random field ζ(t, x), t ∈ Z, x ∈ S n . Estimates are based on observations of the field ζ(t, x) + θ(t, x) at points (t, x), t = − 1, − 2, ..., x ∈ S n , where θ(t, x) is an uncorrelated with ζ(t, x) periodically correlated with respect to time isotropic on the sphere S n random field. Formulas for computing the value of the mean-square error and the spectral characteristic of the optimal linear estimate of the functional are obtained. The least favourable spectral densities and the minimax (robust) spectral characteristics of the optimal estimates of the functional are determined for some special classes of spectral densities.


Random field Prediction Filtering Robust estimate Mean square error Least favourable spectral densities Minimax spectral characteristic 

AMS 2000 Subject Classifications

60G60 62M40 62M20 93E10 93E11 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Iryna Dubovetska
    • 1
  • Oleksandr Masyutka
    • 2
  • Mikhail Moklyachuk
    • 1
    Email author
  1. 1.Department of Probability Theory, Statistics and Actuarial MathematicsKyiv National Taras Shevchenko UniversityKyivUkraine
  2. 2.Department of Mathematics and Theoretical RadiophysicsKyiv National Taras Shevchenko UniversityKyivUkraine

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