By introducing the asymptotic logarithmic likelihood ratio as a measure of Markov approximation of the 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 for functionals of random fields on a uniformly bounded tree are established. Some existing results are generalized in this paper.
WANG Shuai
, YANG Weiguo. , {{custom_author.name_en}}.
A Class of Small Deviation Theorems for Random Fields on a Uniformly Bounded Tree. Journal of Systems Science and Mathematical Sciences, 2010, 30(12): 1631-1642 https://doi.org/10.12341/jssms09436