随机环境中马氏链状态的各种常返性与暂留性
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摘要
考虑到随机环境中马氏链的状态在受到环境因素各种条件的影响下,引入了随机环境中马氏链状态的各种常返性与暂留性概念,讨论了这些常返性与暂留性的相互关系,从而说明随机环境中马氏链状态的常返性与暂留性和经典马氏链状态的常返性与暂留性有着显著的区别.
Several concepts of recurrence and transience of states for Markov Chains in random environments are introduced under the influence of various environmental factors,and their connections and properties are discussed.These conclusions present that the recurrence and transience of states for Markov Chains in random environments and the recurrence and transience of states for classical Markov chains have obvious differences.
Several concepts of recurrence and transience of states for Markov Chains in random environments are introduced under the influence of various environmental factors,and their connections and properties are discussed.These conclusions present that the recurrence and transience of states for Markov Chains in random environments and the recurrence and transience of states for classical Markov chains have obvious differences.
引文
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[11].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.
[12]李应求.双无限环境中马氏链的常返性与不变侧度[J].中国科学A辑,2001,31(8):702-707.
[13]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):1099-1100.
[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,2007,27(2):269-276.
[15]费时龙,任敏.随机环境中马氏链状态的常返性与暂留性[J].高校应用数学报,2011,26(2):187-194.
[16]万成高.随机环境中马氏链函数加权和的极限定理[J].数学物理学报,2015,35A(1):163-171.
[17]宋明珠,吴永锋.马氏双链函数的强大数定律及其应用[J].数学杂志,2015,35(2):368-374.
[18]胡迪鹤.随机环境中的马尔可夫过程[M].北京:高等教育出版社,2011.
[2]Kozlov M V.On the asymptotic behavior of the probability of non-extinction for critical branching processes in a random environment[J].Theory Prob Appl,1976,21(4):742-751.
[3]Alili S.Persistent random walks in stationary environment[J].J Statist Phys,1999,94(3):469-494.
[4]Hong Wenming.Renewal theorem for(L,1)-random walk in random environment[J].Acta Math Sci,2013,33B(6):1736-1748.
[5]Smith W L,Wilkinson W E.On branching processes in random environments[J].Ann Math Statist,1969,40(3):814-827.
[6]李应求,胡杨利,张影.随机环境中两性分枝过程的极限性质[J].中国科学A辑,2015,45(5):611-622.
[7]Nawrotzki K.Finite Markov chains in stationary random environments[J].Ann Probab,1982,10(4):1041-1046.
[8]Cogburn R.Markov Chains in random environments[J].Ann Probab,1980,8(3):908-916.
[9]Cogburn R.The ergodic theory of Markov chains in random environments[J].Z Wahrsch Verw Gebiete,1984,66(2):109-128.
[10]Cogburn R.On direct convergence and periodicity for transition probabilities of Markov chains in random environments[J].Ann Probab,1990,18(2):642-654.
[11].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.
[12]李应求.双无限环境中马氏链的常返性与不变侧度[J].中国科学A辑,2001,31(8):702-707.
[13]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):1099-1100.
[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,2007,27(2):269-276.
[15]费时龙,任敏.随机环境中马氏链状态的常返性与暂留性[J].高校应用数学报,2011,26(2):187-194.
[16]万成高.随机环境中马氏链函数加权和的极限定理[J].数学物理学报,2015,35A(1):163-171.
[17]宋明珠,吴永锋.马氏双链函数的强大数定律及其应用[J].数学杂志,2015,35(2):368-374.
[18]胡迪鹤.随机环境中的马尔可夫过程[M].北京:高等教育出版社,2011.