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 generalizedentropy ergodic theorem for nonhomogeneous Markov chains indexed bya Cayley tree. Firstly, they prove a strong limit theorem for thedelayed sums of the bivariate functions of nonhomogeneous Markovchains indexed by a tree. Secondly, the strong law of large numbersof the frequencies of occurrence of states of delayed sums and thegeneralized entropy ergodic theorem for nonhomogeneous Markov chainsindexed by a Cayley tree are obtained. As corollaries, theygeneralize some known results. The authors also prove that thegeneralized entropy densities for arbitrary finite tree-indexedstochastic processes are uniformly integrable.