Markov approximation of arbitrary random field on homogeneous trees

Abstract

In this article, we establish a class of small deviation theorems for functionals of random fields and the strong law of large numbers for the ordered couple of states for arbitrary random fields on homogenous trees. A known result is generalized in this article.

An Almost Sure Result on Approximation of Homogeneous Random Field from Local Averages

“…Shannon sampling theorem and random field are widely used in all branches of stochastic process, especially, Gaposhkin [22] studied the criteria for the strong law of large numbers for some classes of second-order stationary processes and homogeneous random fields. Yang and Liu [23] gave the strong law of large numbers and Shannon-McMillan theorem for Markov chains fields on trees, and Peng et al [24] researched Markov approximation of arbitrary random field on homogeneous tree. Recently, Zhang et al [25] obtained an upper bound of approximated error of homogeneous random field from local averages in the mean square sense.…”