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1 results

  • Necessary conditions for Markovian processes on a lattice

  • P. A. P. Moran
  • Journal:
    Journal of Applied Probability / Volume 10 / Issue 3 / September 1973
    Published online by Cambridge University Press:
    14 July 2016, pp. 605-612
    Print publication:
    September 1973

  • Stationary processes which are defined on the points of a square lattice and are Markovian in various senses are considered. It is shown that a certain assumption of linearity of regression forces the spectral distribution to be of a certain explicit form, and that given this form Gaussian processes of this kind are easily constructed. Certain non-Gaussian processes satisfying the various Markovian properties are also constructed and the difference from nearest-neighbour systems emphasized. It is conjectured, but not proved, that the assumption of linearity of regression also implies Gaussianity.