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Unilateral Gaussian fields

Part of: Markov processes Special processes

Published online by Cambridge University Press:  01 July 2016

E. M. Tory  and
D. K. Pickard
E. M. Tory*
Affiliation:
Mount Allison University
D. K. Pickard*
Affiliation:
Harvard University
*
∗Postal address: Department of Mathematics and Computer Science, Mount Allison University, Sackville, N.B., EOA 3C0, Canada.
∗∗D. K. Pickard died on 28 July 1986. This joint paper was later completed by E. M. Tory.
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Abstract

The necessary and sufficient condition for unilateral characterization of Gaussian Markov fields and the Besag-Moran positivity condition for second-order autonormal bilateral models define the same tetrahedral domain of achievable regression parameters. A bijective function maps this domain to a different tetrahedral domain of parameters in the Pickard model. These two domains are identical to the corresponding ones in the Welberry-Carroll model. We obtain series solutions for correlation coefficients and study their limits near the boundaries of the first domain.

Keywords

MARKOV FIELDSISING MODELSCRYSTAL GROWTH-DISORDER MODELSUNILATERAL PROCESSESCORRELATIONS OF EMBEDDED MARKOV CHAINS

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 1 , March 1992 , pp. 95 - 112
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported in part by the Natural Sciences and Engineering Research Council of Canada.

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