三元树上非对称马氏链场的强大数定律

Strong law of large numbers for non-symmetric Markov chain field on a three branches tree

定义了一类三元树上非对称马尔可夫链场,利用鞅方法构造鞅,根据Doob鞅收敛定理和一些特殊的不等式以及近年来研究概率论强极限定理的新方法,研究了三元树上非对称马尔可夫链场的强极限定理以及关于状态和状态序偶出现频率的强大数定理,得到了三元树上非对称马尔可夫链场的局部收敛定理以及关于状态和状态序偶出现频率的强大数定理,将三元树上对称马氏链场中的相关结果推广到了三元树上非对称马氏链场中.

The definition of a non-symmetric Markov chain field is given. By applying Martingale and Doob Martingale convergence theorems, some special inequalities and a new technique for establishing the strong limit theorems, the strong limit theorems for non-symmetric Markov chain field on a three branches tree are studied. A local convergence theorem and the strong law of large numbers for non-symmetric Markov chain field are obtained. Some results about the symmetric Markov chain field are extended to the non-symmetric case.