二叉树上分枝马氏链的强大数定理Strong law of large numbers for bifurcating Markov chains indexed by a binary tree
党慧;杨卫国;高荣;石志岩;
摘要(Abstract)：
首先给出了在可列状态空间取值的二叉树上分枝马氏链定义的离散形式,然后建立了二叉树上分枝马氏链的若干强极限定理,最后研究了二叉树上有限状态分枝马氏链的强大数定理.
关键词(KeyWords)： 二叉树;分枝马氏链;强极限定理;强大数定理
基金项目(Foundation): 国家自然科学基金(11071104);; 江苏大学大学生科研立项(12A409)
作者(Authors): 党慧;杨卫国;高荣;石志岩;
参考文献(References)：
- [1]Benjamini I,Peres Y.Markov chains indexed by trees[J].Ann.Probab.,1994,22:219-243.
- [2]Berger T,Ye Z.Entropic aspects of random fields on trees[J].IEEE Trans.Inform.Theory,1990,36:1006-1018.
- [3]Yang W G.Some limit properties for Markov chains indexed by a homogeneous tree[J].Statist.Prob.Lett.,2003,65:241-250.
- [4]Yang W G,Ye Z.The asymptotic equipartition property for nonhomogeneous Markov chains indexed by a homogeneous tree[J].IEEE Trans.Inform.Theory,2007,53:3275-3280.
- [5]Huang H L,Yang W G.Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree[J].Sci.China Ser.A,2008,51:195-202.
- [6]Dong Y,Yang W G,Bai J F.The strong law of large numbers and the Shannon-McMillan theorem for nonhomogeneous Markov chains indexed by a Cayley tree[J].Statist.Probab.Lett.,2011,81:1883-1890.
- [7]Dong Y,Yang W G.Strong law of large numbers and asymptotic equipartition probability for nonsymmetric Markov chain indexed by Cayley tree[J].Mathematical Research Exposition,2010,30(6):976-984.
- [8]Guyon J.Limit theorems for bifurcating Markov chains.Application to the detection of cellular aging[J].Ann.Appl.Probab.,2007,17:1538-1569.