Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T20:49:10.047Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bartlett, M. S. (1967) Inference and stochastic processes. J. R. Statist. Soc. A 130, 457–477.Google Scholar
Bartlett, M. S. (1968) A further note on nearest neighbour models. J. R. Statist. Soc. A 131, 579–580.Google Scholar
Bartlett, M. S. (1971) Two-dimensional nearest-neighbour systems, and their ecological applications. Statistical Ecology. Vol. 1 (in Press).Google Scholar
Bartlett, M. S. and Besag, J. E. (1969) Correlation properties of some nearest-neighbour models. Bull. Int. Statist. Inst. 43, 191–193.Google Scholar
Newell, G. F. and Montroll, E. W. (1953) On the theory of the Ising model of ferromagnetism. Rev. Mod. Phys. 25, 353–389.Google Scholar
Onsager, L. (1944) Crystal statistics I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65, 117–149.Google Scholar
Whittle, P. (1954) On stationary processes in the plane. Biometrika 41, 434–449.CrossRefGoogle Scholar