关于一致有界树上随机场的一类强偏差定理

A CLASS OF SMALL DEVIATION THEOREMS FOR RANDOM FIELDS ON A UNIFORMLY BOUNDED TREE

通过引进渐近对数似然比作为一致有界树上任意随机场关于树指标Markov链逼近的一种度量,通过构造鞅的方法,建立了关于随机场的一类强偏差定理.推广了一些已知的结果.

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.