广义Bethe树图上马氏链场的若干强极限性质  

Some limit properties for Markov chains indexed by generalized Bethe tree

作　　者：杨卫国[1] 马越[1] 黄辉林[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5期413-416,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：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研究了广义Bethe树图上可数状态马氏链场的局部收敛定理.作为推论,得到了此类树图上可数状态马氏链场关于状态与状态序偶出现频率的若干强极限性质和Bethe树图或Cayley树图上可数状态马氏链场关于状态与状态序偶出现频率的强大数定律.Martingale method is employed to investigate a local convergence theorem for countable Markov chains indexed by a generalized Bethe tree by using a martingale and Doob martingale convergence theorem and some special inequalities. As corollaries, some strong limit properties for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by the tree are obtained. The strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by Bethe tree and Cayley tree is also obtained.

关 键 词：概率论 广义Bethe树 马氏链场 状态与状态序偶 强极限定理 鞅收敛定理 

分 类 号：O211.6[理学—概率论与数理统计]