随机环境中马氏链的状态分类及性质
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摘要
本文给出了随机环境中马氏链各种状态的定义,研究了各种状态之间的关系,给出了状态空间的一个划分;同时研究了各状态的性质,最后举例说明了所给状态定义的合理性.
In this paper,various concepts of states for Markov chains in random environments are introduced into the research field,and the relationships between these states are discussed.Especially,a partition of the state space is given.Also,the properties of those states are investigated.At last,some examples are given to illustrate the rationality of those states.
In this paper,various concepts of states for Markov chains in random environments are introduced into the research field,and the relationships between these states are discussed.Especially,a partition of the state space is given.Also,the properties of those states are investigated.At last,some examples are given to illustrate the rationality of those states.
引文
[1]Cogburn R.Markov chains in random environments:the case of Markovian environments[J].Ann.Probab.,1980,8(5):908-916.
[2]Bourgin R D,Cogburn R.On determining absorption probabilities for Markov chains in random environments[J].Adv.in Appl.Probab.,1981,13(2):369-387.
[3]Nawrotzki K.Discrete open systems or Markov chains in a random environmentⅠ[J].Elektron.Informationsverarb.Kybernet,1981,17(11/12):569-599.
[4]Nawrotzki K.Discrete open systems or Markov chains in a random environmentⅡ[J].Elektron.Informationsverarb.Kybernet,1982,18(1/2):83-98.
[5]Cogburn R.The ergodic theory of Markov chains in random environments[J].Z.Wahrsch.Verw.Gebiete,1984,66(1):109-128.
[6]Cogburn R.On direct convergence and periodicity for transition probabilities of Markov chains in random environments[J].Ann.Probab.,1990,18(2):642-654.
[7]Cogburn R.On the central limit theorem for Markov chains in random environments[J].Ann.Probab.,1991,19(2):587-604.
[8]Orey S.Markov chains with stochastically stationary transition probabilities[J].Ann.Probab.,1991,19(3):907-928.
[9]Kifer Y.Limit theorems for random transformations and processes in random environments[J].Trans.Amer.Math.Soc,1998,350(4):1481-1518.
[10]胡迪鹤.从p-m链到随机环境中的马氏链[J].数学年刊,2004,25A(1):65-78.
[11]Li Y Q.Recurrence and invariant measure of Markov chains in double-infinite random environments[J].Sci.China Ser.A,2001,44(10):1294-1299.
[12]李应求.双无限环境中马氏链的存在和不可约性[J].数学物理学报,2001,21A(4):439-442.
[13]李应求,王苏明,胡杨利.随机环境中马氏链与马氏双链问的相互关系[J].数学学报,2006,49(6):1373-1380.
[14]李应求.双无限随机环境中马氏链的暂留性[J].数学物理学报,2007,27A(2):269-276.
[15]李应求.双无限随机环境中的常返马氏链[J].数学学报,2007,50(5):1099-1110.
[16]汪和松,李应求,王众.双无限环境中马氏链的常返和暂留性[J].系统科学与数学,2009,29(3):418-424.
[17]李应求,汪和松,王众.马氏环境中马氏链转移概率几何平均及其泛函的强极限定理[J].数学物理学报,2011,31A(2):508-517.
[18]肖争艳,胡迪鹤.绕积马氏链的状态分类[J].数学物理学报,2003,23A(3):306-313.
[19]李应求.随机环境中马氏链与两参数马氏过程(武汉大学博士后研究工作报告)[R].武汉:武汉大学,2001.
[2]Bourgin R D,Cogburn R.On determining absorption probabilities for Markov chains in random environments[J].Adv.in Appl.Probab.,1981,13(2):369-387.
[3]Nawrotzki K.Discrete open systems or Markov chains in a random environmentⅠ[J].Elektron.Informationsverarb.Kybernet,1981,17(11/12):569-599.
[4]Nawrotzki K.Discrete open systems or Markov chains in a random environmentⅡ[J].Elektron.Informationsverarb.Kybernet,1982,18(1/2):83-98.
[5]Cogburn R.The ergodic theory of Markov chains in random environments[J].Z.Wahrsch.Verw.Gebiete,1984,66(1):109-128.
[6]Cogburn R.On direct convergence and periodicity for transition probabilities of Markov chains in random environments[J].Ann.Probab.,1990,18(2):642-654.
[7]Cogburn R.On the central limit theorem for Markov chains in random environments[J].Ann.Probab.,1991,19(2):587-604.
[8]Orey S.Markov chains with stochastically stationary transition probabilities[J].Ann.Probab.,1991,19(3):907-928.
[9]Kifer Y.Limit theorems for random transformations and processes in random environments[J].Trans.Amer.Math.Soc,1998,350(4):1481-1518.
[10]胡迪鹤.从p-m链到随机环境中的马氏链[J].数学年刊,2004,25A(1):65-78.
[11]Li Y Q.Recurrence and invariant measure of Markov chains in double-infinite random environments[J].Sci.China Ser.A,2001,44(10):1294-1299.
[12]李应求.双无限环境中马氏链的存在和不可约性[J].数学物理学报,2001,21A(4):439-442.
[13]李应求,王苏明,胡杨利.随机环境中马氏链与马氏双链问的相互关系[J].数学学报,2006,49(6):1373-1380.
[14]李应求.双无限随机环境中马氏链的暂留性[J].数学物理学报,2007,27A(2):269-276.
[15]李应求.双无限随机环境中的常返马氏链[J].数学学报,2007,50(5):1099-1110.
[16]汪和松,李应求,王众.双无限环境中马氏链的常返和暂留性[J].系统科学与数学,2009,29(3):418-424.
[17]李应求,汪和松,王众.马氏环境中马氏链转移概率几何平均及其泛函的强极限定理[J].数学物理学报,2011,31A(2):508-517.
[18]肖争艳,胡迪鹤.绕积马氏链的状态分类[J].数学物理学报,2003,23A(3):306-313.
[19]李应求.随机环境中马氏链与两参数马氏过程(武汉大学博士后研究工作报告)[R].武汉:武汉大学,2001.