Physical nearest-neighbour models and non-linear time-series
- 1 June 1971
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 8 (2) , 222-232
- https://doi.org/10.2307/3211892
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.Keywords
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