Necessary conditions for Markovian processes on a lattice
- 1 September 1973
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 10 (3) , 605-612
- https://doi.org/10.2307/3212780
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
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