Cayley树上非对称马氏链的强大数定律及渐近均分割性

Strong Law of Large Numbers and Asymptotic Equipartition Probability for Nonsymmetric Markov Chain Indexed by Cayley Tree

中文关键词:  强大数定律  非对称马氏链  Cayley树  渐近均分割性.

英文关键词:strong law of large numbers  nonsymmetric Markov chain  Cayley tree  asymptotic equipartition property.

中文摘要:

      本文通过构造鞅的方法,研究了Cayley树上非对称马氏链的状态及状态序偶出现频率的强大数定律,从而得到了其几乎处处收敛的渐近均分割性定理,所得结果推广了一个已知结果.

英文摘要:

      In this paper, we study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain (NSMC) indexed by Cayley tree with any finite states. The asymptotic equipartition properties with almost everywhere (a.e.) convergence for NSMC indexed by Cayley tree are obtained. This article generalizes a recent result.