Some problems of linear prediction of homogeneous and isotropic fields using functionals of a given type
Applied Topics in Control Theory and Mathematical Cybernetics
Received:
Abstract
We consider the problem of prediction of a homogeneous and isotopic random field inside a sphere from observations outside the sphere. The solution is sought in the form of a linear functional of the observations. Equations are deried for the optimal parameter values of this linear functional.
Keywords
Optimal Parameter Random Field Linear Prediction Isotropic Field
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
Literature cited
- 1.H. Bateman and A. Erdelyi, Higher Transcendental Functions [Russian translation], Mir, Moscow (1966).Google Scholar
- 2.I. I. Gikhman and A. V. Skorokhod, An Introduction to the Theory of Stochastic Processes [in Russian], Nauka, Moscow (1977).Google Scholar
- 3.M. E. Zyukov, “On extrapolation of homogeneous and isotropic random fields by a functional of a given type,” Vychisl. Prikl. Mat., No. 30, 32–37 (1976).Google Scholar
- 4.M. I. Yadrenko, Spectral Theory of Stochastic Proceses [in Russian], Vishcha Shkola, Kiev (1980).Google Scholar
- 5.D. R. Cox, “Prediction by exponentially weighted moving averages and related methods,” J. R. Stat. Soc., Ser. B,23, 414–422 (1961).Google Scholar
- 6.L. Yudell, Integrals of Bessel Functions, Midwest Res. Inst., New York (1902).Google Scholar
Copyright information
© Plenum Publishing Corporation 1992