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Homogeneous Gaussian Markov processes on general lattices

Part of: Acceleration of convergence Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Fumiyasu Komaki
Fumiyasu Komaki*
Affiliation:
Institute of Statistical Mathematics, Tokyo
*
* Postal address: The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu Minato-ku, Tokyo 106, Japan.
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Abstract

A homogeneous Gaussian Markov lattice-process model has a regression coefficient that determines the extent to which a random variable of a vertex is dependent on those of the neighbors. In many studies, the absolute value of this parameter has been assumed to be less than the reciprocal of the number of neighbors. This condition is shown to be necessary and sufficient for the existence of the Gaussian process satisfying the model equations under some assumptions on lattices using the notion of dual processes. We also give examples of models that neither satisfy the condition imposed on the region for the parameter nor the assumptions on lattices. A formula for autocovariance functions of Gaussian Markov processes on general lattices is derived, and numerical procedures to calculate the autocovariance functions are proposed.

Keywords

AUTOCOVARIANCE FUNCTIONSCAR PROCESSESDUAL PROCESSESNUMERICAL APPROXIMATION OF THE AUTOCOVARIANCEADMISSIBLE REGION FOR PARAMETERS

MSC classification

Primary: 60G60: Random fields 62M40: Random fields; image analysis
Secondary: 65B99: None of the above, but in this section
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 28 , Issue 1 , March 1996 , pp. 189 - 206
Copyright
Copyright © Applied Probability Trust 1996 

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