关键词: Cayley树上的马尔可夫链场;样本相对熵率;小偏差定理;强偏差定理;强极限定理

Abstract:

 By introducing the sample relative entropy rate as a measure of the deviation bewteen the arbitrary random fields and the Markov chain fields on Cayley trees, a class of small deviation theorems  for the frequencies of state ordered couples  are established. In the proof a new analytic technique in the study of the strong limit theorems for Markov chains is applied.

Key words:  Markov chain fields on Cayley trees, Sample relative entropy rate, Small deviation theorem, Strong deviation theorem, Strong limit theorem