马氏环境中树指标马氏链随机转移概率调和平均的强极限性质  

A LIMIT PROPERTY OF RANDOM TRANSITION PROBABILITY FOR A MARKOV CHAIN INDEXED BY A TREE IN MARKOVIAN ENVIRONMENT

作　　者：石志岩[1] 鲍丹 吴佰慧 SHI Zhi-yan;BAO Dan;WU Bai-hui(School of Science,Jiangsu University,Zhenjiang 212013,China)

机构地区：[1]江苏大学理学院

出　　处：《数学杂志》2019年第4期575-582,共8页Journal of Mathematics

基　　金：国家自然科学基金(11601191;11571142);江苏大学青年英才计划

摘　　要：本文研究了离散状态下随机环境中树指标马氏链,证明了该过程在概率空间中可以实现,同时阐明了马氏环境下树指标马氏链与树指标马氏双链的等价性.获得了有限状态下马氏环境中树指标马氏链的随机转移概率调和平均的强极限性质.In this paper, we study the tree-indexed Markov chain in random environment under discrete state and prove the realization of this stochastic process in the probability space. Meanwhile, the equivalence between tree-indexed Markov chains in Markov environment and tree-indexed Markov double chains is provided in this paper. Finally, the strong limit property of the harmonic mean of the random transition probability of tree indexed Markov chain in the Markovian environment is obtained under the finite state.

关 键 词：马氏环境 马氏链 随机转移概率 调和平均 

分 类 号：O211.6[理学—概率论与数理统计]