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[ai-geostats] A detail in the derivation of Whittle-Matern spatil correlation function

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  • Ruben Roa Ureta
    Hi: I hope my question is not considered offtopic. It concerns with an aspect of the mathematical theory of the spatial autocorrelation function. In his 1954
    Message 1 of 1 , Apr 25, 2005
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      Hi:
      I hope my question is not considered offtopic. It concerns
      with an aspect of the mathematical theory of the spatial
      autocorrelation function. In his 1954 Biometrika paper*, on
      stationary processes in the plane, Whittle demonstrated that
      the natural extension of the time series theory to spatial
      series led to a correlation function involving the modified
      Bessel function of the second kind. A key step in the reasoning
      is the approximation of the difference equation with a
      differential equation (actually a generalization of Laplace's
      equation). My doubt arises just before that step, in the transit
      from eq. (62) to eq. (63). It is straightforward to
      derive the equivalence of these two equations but i believe
      the random term on the rhs has changed its moments,
      though Whittle may have thought trivial to say so. Anyone
      cares to look at this and tell me if i am correct?
      Cheers
      Ruben

      *Whittle. 1954. On stationary processes in the plane. Biometrika
      41:434-439.
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