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
MathematicsNearest neighbourStatistical physicsSeries (stratigraphy)Markov chainLattice (music)Applied mathematicsStatisticsComputer science
Affiliated Institutions
Related Publications
Estimation and Model Identification for Continuous Spatial Processes
SUMMARY Formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced. The processes are assumed to be adequately descri...
Approximate Inference in Generalized Linear Mixed Models
Statistical approaches to overdispersion, correlated errors, shrinkage estimation, and smoothing of regression relationships may be encompassed within the framework of the gener...
Estimation in generalized linear models with random effects
A conceptually very simple but general algorithm for the estimation of the fixed effects, random effects, and components of dispersion in generalized linear models with random e...
Two-dimensional Hubbard model: Numerical simulation study
We have studied the two-dimensional Hubbard model on a square lattice with nearest-neighbor hopping. We first discuss the properties of the model within the mean-field approxima...
Some Asymptotic Results on Generalized Penalized Spline Smoothing
Summary The paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size. The proof is provided in a generalized smooth...
Publication Info
- Year
- 1971
- Type
- article
- Volume
- 8
- Issue
- 2
- Pages
- 222-232
- Citations
- 77
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
77
OpenAlex
1
Influential
51
CrossRef
Cite This
M. S. Bartlett
(1971).
Physical nearest-neighbour models and non-linear time-series.
Journal of Applied Probability
, 8
(2)
, 222-232.
https://doi.org/10.2307/3211892
Identifiers
- DOI
- 10.2307/3211892