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Journal Article

Physical Nearest-Neighbour Models and Non-Linear Time-Series

M. S. Bartlett
Journal of Applied Probability
Vol. 8, No. 2 (Jun., 1971), pp. 222-232
DOI: 10.2307/3211892
Stable URL: http://www.jstor.org/stable/3211892
Page Count: 11
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Physical Nearest-Neighbour Models and Non-Linear Time-Series
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Abstract

A general class of spatial-temporal Markov processes is defined leading to the standard spatial equilibrium distribution for nearest-neighbour models on a multi-dimensional lattice. Physical properties are obtainable from the marginal spatial spectral function. However, only the simplest one-dimensional case corresponds to a linear model with a readily derived spectrum. Non-linear models corresponding to two- and three-dimensional lattices are presented in their simplest terms, and a preliminary discussion of approximate solutions is included.

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