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Necessary conditions for Markovian processes on a lattice

Published online by Cambridge University Press:  14 July 2016

P. A. P. Moran
P. A. P. Moran*
Affiliation:
The Australian National University
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Abstract

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.

Keywords

MARKOV PROCESSES ON LATTICESSPECTRAL THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 605 - 612
Copyright
Copyright © Applied Probability Trust 1973 

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