非齐次树上非齐次马氏链的一个强偏差定理
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摘要
树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强偏差定理一直是国际概率论界研究的中心课题之一.本文利用Doob鞅收敛定理研究给出了非齐次树上m重非齐次马氏链关于广义赌博系统的强偏差定理.
In recent years, tree indexed stochastic process has become one of the hot topics in probability theory. The strong deviation theorem has been one of the central issues of the international probability theory. In this paper, through applying Doob's martingale convergence theorem, a strong deviation theorem on the generalized gambling system for m-ordered non-homogeneous Markov chain on a non-homogeneous tree is given.
In recent years, tree indexed stochastic process has become one of the hot topics in probability theory. The strong deviation theorem has been one of the central issues of the international probability theory. In this paper, through applying Doob's martingale convergence theorem, a strong deviation theorem on the generalized gambling system for m-ordered non-homogeneous Markov chain on a non-homogeneous tree is given.
引文
[1]韩大钊,石志岩,杨卫国.树上路径过程的随机路径条件概率的强极限定理[J].数学杂志,2015,35(2):462-468.
[2]张泓知,郝瑞丽,叶中行,等.可列非齐次马氏链的强极限性质[J].应用概率统计,2016,32(1):62-68.
[3]Shi Z Y,Yang W G.The definition of tree-indexed Markov chains in random environment and their existence[J].Communications in Statistics-Theory and Methods,2017,46(16):7934-7941.
[4]Dang H,Shi Z Y,Yang W G.The strong law of large numbers and the entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree[J].IEEE Transactions on Information Theory,2015,61(4):1640-1648.
[5]Shi Z Y,Yang W G.Strong laws of large numbers for the mth-order asymptotic odd-even Markov chains indexed by an m-rooted Cayley tree[J].Communications in Statistics-Theory and Methods,2017,46(4):1855-1870.
[6]Huang H L,Yang W G,Shi Z Y.Asymptotic equipartition property for second-order circular Markov chains indexed by a two-rooted Cayley tree[J].Communications in Statistics-Theory and Methods,2017,46(3):1275-1289.
[7]刘建国,杨卫国.关于可列马氏链状态出现频率延迟平均的强大数定律[J].经济数学,2017,34(1):65-67.
[8]金少华,刘璐,陈秀引.非齐次树上m重非齐次马氏信源的一个强偏差定理[J].数学的实践与认识,2017,47(9):258-267.
[2]张泓知,郝瑞丽,叶中行,等.可列非齐次马氏链的强极限性质[J].应用概率统计,2016,32(1):62-68.
[3]Shi Z Y,Yang W G.The definition of tree-indexed Markov chains in random environment and their existence[J].Communications in Statistics-Theory and Methods,2017,46(16):7934-7941.
[4]Dang H,Shi Z Y,Yang W G.The strong law of large numbers and the entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree[J].IEEE Transactions on Information Theory,2015,61(4):1640-1648.
[5]Shi Z Y,Yang W G.Strong laws of large numbers for the mth-order asymptotic odd-even Markov chains indexed by an m-rooted Cayley tree[J].Communications in Statistics-Theory and Methods,2017,46(4):1855-1870.
[6]Huang H L,Yang W G,Shi Z Y.Asymptotic equipartition property for second-order circular Markov chains indexed by a two-rooted Cayley tree[J].Communications in Statistics-Theory and Methods,2017,46(3):1275-1289.
[7]刘建国,杨卫国.关于可列马氏链状态出现频率延迟平均的强大数定律[J].经济数学,2017,34(1):65-67.
[8]金少华,刘璐,陈秀引.非齐次树上m重非齐次马氏信源的一个强偏差定理[J].数学的实践与认识,2017,47(9):258-267.