Description of Random Fields by Means of One-Point Conditional Distributions and Some Applications

S. Dachian, B.S. Nahapetian

2001, v.7, №2, 193-214

ABSTRACT

The problem of description of random fields by means of one-point conditional distributions is considered. A necessary and sufficient condition for a given system of one-point distributions with boundary conditions to be a subsystem of some specification is given. A sufficient condition for existence of random fields with given one-point conditional distributions, as well as some applications concerning Gibbs description of random fields, non-Gibbsian random fields and martingale-difference random fields are presented.

Keywords: random fields,conditional probabilities,one-point systems,Gibbs distributions

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