奇偶树上马氏链场的强大数定律

Strong law of large numbers for Markov chain fields on an even-odd tree

定义一类非齐次树——奇偶树,利用近年来研究概率论强极限定理的新方法,研究奇偶树上奇偶马氏链场关于状态和状态序偶出现频率的强极限定理,得到奇偶树上马氏链场关于状态和状态序偶出现频率的强大数定律,将齐次树图上马氏链场中的相关结果推广到了非齐次树图上.

The definition of a nonhomogeneous tree called an even-odd tree is given. By applying a new technique for establishing the strong limit theorems in probability theory in recent years, the strong limit theorems on the frequencies of occurrence of states and ordered couples of states for even-odd Markov chains indexed by a nonhomogeneous tree are studied. The strong law of large numbers for Markov chains indexed by an even-odd tree is obtained. Some results about the Markov chains indexed by a homogeneous tree are extended to the Markov chains indexed by a nonhomogeneous tree.