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arXiv · 2202.09158

Description of random fields by systems of conditional distributions

L. A. Khachatryan
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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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L. A. Khachatryan. 2022-02-18. Description of random fields by systems of conditional distributions. https://doi.org/10.52737/18291163-2022.14.8-1-40

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