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Physical nearest-neighbour models and non-linear time-series

Published online by Cambridge University Press:  14 July 2016

M. S. Bartlett
M. S. Bartlett*
Affiliation:
University of Oxford
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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.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 2 , June 1971 , pp. 222 - 232
Copyright
Copyright © Applied Probability Trust 1971 

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References

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