关于齐次树上随机场的一类强偏差定理

A CLASS OF SMALL DEVIATION THEOREMS FOR RANDOM FIELDS ON A HOMOGENEOUS TREE

通过引进渐近对数似然比作为齐次树上任意Markov随机场逼近的一种度量,通过构造鞅的方法,建立了关于随机场的一类强偏差(也称小偏差)定理.所得结论推广了一个已知的结果.

By introducing the asymptotic logarithmic likelihood ratio as a measure of Markov approximation of the arbitrary random field on a homogeneous tree, and constructing a non-negative martingale, a class of small deviation theorems for random fields is established, and an existing result is generalized.