M阶非齐次马氏链随机转移概率调和平均的一类强极限定理  

Strong Limit Theorems for Harmonic Mean of Transition Probability of Mth-Order Nonhomogeneous Markov Information Source

作　　者：叶慧[1] 

机构地区：[1]江苏科技大学数理学院,江苏镇江212003

出　　处：《数学的实践与认识》2011年第22期215-221,共7页Mathematics in Practice and Theory

摘　　要：主要研究任意m阶非齐次马氏链的随机转移概率调和平均的a.s.收敛的强极限定理.在证明中采用了一种把网微分法与条件矩母函数相结合应用于马氏链强极限定理研究的新途径.作为推论,得到m阶非齐次马氏链的一个公平比的强极限定理,并将已有的结果加以推广.In this paper, we study the strong limit theorems on the a.s. convergence for the harmonic mean of the ruth-order nonhomogeneous Markov chain. In the proof, we apply the tools of the conditional moment generating functions and the differentiation on a net to the study of strong limit theorems for the mth-order nonhomogeneous Markov chain. As corollaries, a limit theorem for fair ratio of ruth-order nonhomogeneous Markov chains is obtained. Moreover, the results which have been obtained are generalized.

关 键 词：m阶非齐次马氏链 调和平均 网微分法 条件矩母函数. 

分 类 号：O211.4[理学—概率论与数理统计]