非齐次树上马氏双链的一个强极限定理
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摘要
树指标随机过程已成为近年发展起来的概率论的研究方向之一.强极限定理一直是国际概率论界研究的中心课题之一.通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,研究给出了一类非齐次树上马氏双链的一个强极限定理.
In recent years, tree indexed stochastic process has become one of the hot topics in probability theory. The strong limit theorem has been one of the central issues of the international probability theory. In this paper, through constructing a non-negative martingale and applies Doob′s martingale convergence theorem to the research of a.e. convergence, a strong limit theorem about double Markov chains on a non-homogenous tree is given.
In recent years, tree indexed stochastic process has become one of the hot topics in probability theory. The strong limit theorem has been one of the central issues of the international probability theory. In this paper, through constructing a non-negative martingale and applies Doob′s martingale convergence theorem to the research of a.e. convergence, a strong limit theorem about double Markov chains on a non-homogenous tree is given.
引文
[1]金少华,卢芳,陈秀引,等.非齐次树上马氏信源的一类Shannon-Mc Millan定理[J].纯粹数学与应用数学,2014,30(4):331-340.
[2]Dong Y,Yang W G,Bai J F.The strong law of large numbers and the Shannon-Mc Millan theorem for nonhomogeneous Markov chains indexed by a Cayley tree[J].Statistics and Probability Letters,2011,81:1883-1890.
[3]党慧,杨卫国,高荣,等.二叉树上分枝马氏链的强大数定理[J].纯粹数学与应用数学,2013,29(5):529-535.
[4]Shi Z Y,Yang W G.Some limit properties for the m-th-order non-homogeneous Markov chains indexed by an m rooted Cayley tree[J].Statistics and Probability Letters,2010,80(15):1223-1233.
[5]Yang W G.A class of deviation theorems for the random fields associated with non-homogeneous Markov chains indexed by a Bethe tree[J].Stochastic Analysis and Applications,2012,30(2):220-237.
[6]金少华,王东,王永生,等.关于树上连续状态马氏泛函的一类强偏差定理[J].数学的实践与认识,2014,44(1):212-217.
[7]宋明珠.马氏双链函数的一个强大数定律[J].数学杂志,2012,32(6):1105-1110.
[2]Dong Y,Yang W G,Bai J F.The strong law of large numbers and the Shannon-Mc Millan theorem for nonhomogeneous Markov chains indexed by a Cayley tree[J].Statistics and Probability Letters,2011,81:1883-1890.
[3]党慧,杨卫国,高荣,等.二叉树上分枝马氏链的强大数定理[J].纯粹数学与应用数学,2013,29(5):529-535.
[4]Shi Z Y,Yang W G.Some limit properties for the m-th-order non-homogeneous Markov chains indexed by an m rooted Cayley tree[J].Statistics and Probability Letters,2010,80(15):1223-1233.
[5]Yang W G.A class of deviation theorems for the random fields associated with non-homogeneous Markov chains indexed by a Bethe tree[J].Stochastic Analysis and Applications,2012,30(2):220-237.
[6]金少华,王东,王永生,等.关于树上连续状态马氏泛函的一类强偏差定理[J].数学的实践与认识,2014,44(1):212-217.
[7]宋明珠.马氏双链函数的一个强大数定律[J].数学杂志,2012,32(6):1105-1110.