Armenian Journal of Mathematics, 14(8)
2022; 1–40
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Description of random fields by systems of conditional distributions

Linda Khachatryan*

Received: 2024-12-05 · Published: 2022-06-03

© 2022 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Description of random fields by systems of conditional distributions
Author
Linda Khachatryan
Source journal
Armenian Journal of Mathematics, 14(8)
Published
2022-06-03
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/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.
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