关于树指标非齐次马氏链的广义熵遍历定理

主要研究了树指标非齐次马氏链的广义熵遍历定理.首先证明了树指标非齐次马氏链上的二元函数延迟平均的强极限定理.然后得到了树指标非齐次马氏链上状态出现延迟频率的强大数定律,以及树指标非齐次马氏链的广义熵遍历定理.作为推论,推广了一些已有结果.同时,证明了局部有限无穷树树指标有限状态随机过程广义熵密度的一致可积性.

The Generalized Entropy Ergodic Theorem for Nonhomogeneous Markov Chains Indexed by a Cayley Tree

In this paper, the authors study the generalized entropy ergodic theorem for nonhomogeneous Markov chains indexed by a Cayley tree. Firstly, they prove a strong limit theorem for the delayed sums of the bivariate functions of nonhomogeneous Markov chains indexed by a tree. Secondly, the strong law of large numbers of the frequencies of occurrence of states of delayed sums and the generalized entropy ergodic theorem for nonhomogeneous Markov chains indexed by a Cayley tree are obtained. As corollaries, they generalize some known results. The authors also prove that the generalized entropy densities for arbitrary finite tree-indexed stochastic processes are uniformly integrable.