A class of small deviation theorems for random fields on a uniformly bounded tree

摘要

By introducing the asymptotic logarithmic likelihood ratio as a measure of the Markov approximation of arbitrary random fields on a uniformly bounded tree, by constructing a non-negative martingale on a uniformly bounded tree, a class of small deviation theorems of functionals and a class of small deviation theorems of the frequencies of occurrence of states for random fields on a uniformly bounded tree are established. Some known results are generalized in this paper. MSC:60J10, 60F15.