Unilateral models for stochastic lattice processes

2006 ◽  
pp. 268-281
Author(s):  
Dag Tjøstheim
Keyword(s):  
Lattice Processes

On the variance of the sample correlation between two independent lattice processes

1981 ◽  
Vol 18 (04) ◽  
pp. 943-948 ◽  
Author(s):  
Sylvia Richardson ◽  
Denis Hemon
Keyword(s):  
Wide Class ◽  
Asymptotic Expression ◽  
Asymptotic Variance ◽  
First Order ◽  
Sample Correlation ◽  
Lattice Processes ◽  
Independent Lattice

Consider two stochastically independent, stationary Gaussian lattice processes with zero means, {X(u), u (Z 2} and {Y(u), u (Z 2}. An asymptotic expression for the variance of the sample correlation between {X(u)} and {Y(u)} over a finite square is derived. This expression also holds for a wide class of domains in Z 2. As an illustration, the asymptotic variance of the correlation between two first-order autonormal schemes is evaluated.

On the estimation and testing of spatial interaction in Gaussian lattice processes

Biometrika ◽  
1975 ◽  
Vol 62 (3) ◽  
pp. 555-562 ◽  
Author(s):  
J. E. BESAG ◽  
P. A. P. MORAN
Keyword(s):  
Spatial Interaction ◽  
Lattice Processes

The principle of the diffusion of arbitrary constants

1972 ◽  
Vol 9 (3) ◽  
pp. 519-541 ◽  
Author(s):  
Andrew D. Barbour
Keyword(s):  
Central Limit ◽  
Continuous Time ◽  
Large Population ◽  
Biological Models ◽  
Deterministic Solution ◽  
Lattice Processes

Equations are derived describing a central limit type large population approximation for continuous time Markov lattice processes in one or more dimensions, such as are commonly encountered in biological models. A method of solving the equations using only the deterministic solution of the process is explained, and it is extended by the use of a martingale argument to provide more detailed information about the process.

Enhancement of Rare‐Earth Ion Fluorescence by Lattice Processes in Oxides

1962 ◽  
Vol 36 (7) ◽  
pp. 1793-1796 ◽  
Author(s):  
L. G. Van Uitert ◽  
R. R. Soden ◽  
R. C. Linares
Keyword(s):  
Rare Earth ◽  
Rare Earth Ion ◽  
Lattice Processes

Statistical spatial series modelling II: Some further results on unilateral lattice processes

1983 ◽  
Vol 15 (3) ◽  
pp. 562-584 ◽  
Author(s):  
Dag Tjøstheim
Keyword(s):  
Time Series ◽  
Half Space ◽  
Special Interest ◽  
Asymptotic Theory ◽  
Innovation Process ◽  
Asymptotic Results ◽  
Practical Applications ◽  
Spatial Series ◽  
Lattice Processes ◽  
Series Criteria

An asymptotic theory of estimation is developed for classes of spatial series F(x1, · ··, xn), where (x1, · ··, xn) varies over a regular cartesian lattice. Two classes of unilateral models are studied, namely half-space models and causal (quadrant-type) models. It is shown that a number of asymptotic results are common for these models. Of special interest for practical applications is the problem of determining how many parameters should be included to describe the degree of dependence in each direction. Here we are able to obtain weakly consistent generalizations of familiar time-series criteria under the assumption that the generating variables of the model are independently and identically distributed. For causal models we introduce the concepts of spatial innovation process and lattice martingale and use these to extend some of the asymptotic theory to the case where a certain type of dependence is permitted in the generating variables.

scholarly journals Goodness of fit for lattice processes

2009 ◽  
Vol 151 (2) ◽  
pp. 113-128 ◽  
Author(s):  
Javier Hidalgo
Keyword(s):  
Goodness Of Fit ◽  
Lattice Processes
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