关于二重有限非齐次马氏链的强大数定律  

Strong laws of large numbers for second order finite nonhomogeneous Markov chains

作　　者：杨卫国[1] 刘杰[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）》2009年第2期209-212,共4页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10571076)

摘　　要：利用鞅方法给出二重有限非齐次马氏链关于状态序偶出现频率的强大数定理.首先,利用鞅差序列收敛定理得到二重有限非齐次马氏链的k元函数一类平均值的一个强极限定理;随后,将已有文献中的二元状态序偶出现频率的平均值的极限定理加以推广,得到任意k元的情况;最后作为推论,得到一系列相关状态序偶出现频率的一类强极限定理.The method of martingale is used to give strong laws of large numbers on frequency occurence of the states for second order finite nonhomogenous Markov chains.First,a limit theorem for averages of the functions of k variables of second order nonhomogeneous Markov chains is established by the convergence theorem for martingale difference sequence.Then,the limit theorems existed in bibliography for averages of frequency of occurrence of two states are generized to the case of arbitrary k.Finally,as corollaries,a series of strong limit theorems for frequency of occurrence of states are obtained.

关 键 词：二重非齐次马氏链 鞅 强大数定理 状态序偶出现频率 

分 类 号：O211.6[理学—概率论与数理统计]