关于任意Cayley树上马尔可夫链场的一类强大数定律

Strong Large Number Law for Markov Chains Field on Arbitrary Cayley Tree

主要研究任意Cayley树上马尔可夫链场的状态出现频率的强大数定律以及Cayley树上任意函数的一类强大数定律。作为推论得到了已有的结果,在证明中采用了一种研究强极限定理的新方法。

The strong law of large numbers for the state frequency and the strong limit theorem of arbitrary function for the Markov chain field on the arbitrary Cayley tree are investigated. As corollaries, some existed results are obtained. A new method in the deduction of the strong limit theorem is adopted.