Description of random fields by systems of conditional distributions

Linda Khachatryan

doi:10.52737/18291163-2022.14.8-1-40

Authors

Linda Khachatryan Institute of Mathematics, National Academy of Science of RA

DOI:

https://doi.org/10.52737/18291163-2022.14.8-1-40

Keywords:

Random field, conditional distribution, specification, Markov random field

Abstract

In this paper, we consider the direct and inverse problems of the description of lattice positive random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions. In the majority of cases, we provide necessary and sufficient conditions for the system to be a conditional distribution of a (unique) random field. The exception is Dobrushin-type systems for which only sufficient conditions are known. Also, we discuss possible applications of the considered systems.

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