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

作　　者：杨卫国[1] 黄辉林[1] 马越[1] 

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2005年第3期244-247,共4页Journal of Jiangsu University：Natural Science Edition

基　　金：江苏省教育厅自然科学基金资助项目(02KJD110003)

摘　　要：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.

关 键 词：非齐次树 状态 状态序偶 马氏链场 强大数定律 

分 类 号：O211.6[理学—概率论与数理统计]