English

Description of random fields by systems of conditional distributions

Probability 2022-06-06 v2

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.

Keywords

Cite

@article{arxiv.2202.09158,
  title  = {Description of random fields by systems of conditional distributions},
  author = {L. A. Khachatryan},
  journal= {arXiv preprint arXiv:2202.09158},
  year   = {2022}
}

Comments

27 pages

R2 v1 2026-06-24T09:44:19.366Z