Description of random fields by systems of conditional distributions
arXiv:2202.09158 · doi:10.52737/18291163-2022.14.8-1-40
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.
27 pages