Description of random fields by means of one-point conditional distributions and some applications (Q2758441)
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scientific article; zbMATH DE number 1679857
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Description of random fields by means of one-point conditional distributions and some applications |
scientific article; zbMATH DE number 1679857 |
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23 May 2002
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random fields
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conditional probabilities
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one-point systems
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Gibbs distributions
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Description of random fields by means of one-point conditional distributions and some applications (English)
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The authors propose a solution of Dobrushin's problem of description of random fields by means of one-point conditional distributions. The case of so-called weakly positive or vacuum specifications with finite state spaces are considered. The authors give a necessary and sufficient consistency condition for a given system of one-point distributions with boundary conditions to be a subsystem of some specification. Sufficient conditions for the existence of a random field with given one-point conditional distributions are given. The cases of non-Gibbsian random fields and martingale-difference random fields are considered.
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