Description of random fields by systems of conditional distributions

L. A. Khachatryan

Published 2022-02-18Version 1

In this paper, we consider the direct and inverse problems of the description of 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 the possible applications of the considered systems.