多重随机环境中的马尔可夫链
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摘要
引入了多重随机环境中的马尔可夫链,讨论了多重随机环境中的马尔可夫链的若干性质,给出了多重随机环境中的马尔可夫链的几个应用背景.证明了多重随机环境中的马尔可夫链的一个存在性定理,获得了多重随机环境中的马尔可夫链若干等价描述.
The multiple Markov chains in random environments were introduced and several properties and application backgrounds of the multiple Markov chains in random environments were given.An existence theorem on the multiple Markov chains in random environments was proved and several equivalent conditions of the multiple Markov chains in random environments were presented.
The multiple Markov chains in random environments were introduced and several properties and application backgrounds of the multiple Markov chains in random environments were given.An existence theorem on the multiple Markov chains in random environments was proved and several equivalent conditions of the multiple Markov chains in random environments were presented.
引文
[1]SZASE D,TOTH B.Peresist random walks in one-dimensional random environment[J].Journal of Statistical Physics,1984,37(1):28-38.
[2]SOLOMN F.Random walks in a random environment[J].Ann Probab,1975,3(1):1-31.
[3]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.
[4]ALILI S.Persistent random walks in stationary environment[J].Journal of Statistical Physics,1999,94(3):469-494.
[5]SMITH W L,WILKINSON W E.On branching processes in random environments[J].Ann Math Statist,1969,40(3):814-827.
[6]胡杨利,吴庆平,李应求.随机环境中依赖年龄分枝过程的爆炸问题[J].数学学报A辑,2010,53(5):1027-1034.
[7]COGBURN R.Markov Chains in random environments[J].Ann Probab,1980,8(3):908-916.
[8]COGBURN R.The ergodic theory of Markov chains in random environments[J].Z W,1984,66(2):109-128.
[9]COGBURN R.On direct convergence and periodicity for transition probabilities of Markov chains in random environments[J].Ann Probab,1990,18(2):642-654.
[10]COGBURN R.On the central limit theorem for Markov chains in random environments[J].Ann Probab,1991,19(2):587-604.
[11]OREY S.Markov chains with stochastically stationary transition probabilities[J].Ann Probab,1991,19(3):907-928.
[12]丁万鼎.关于随机环境中的马尔可夫链的马氏性[J].安徽师大学报,1986,(4):1-5.
[13]胡迪鹤.随机环境中q-过程的存在唯一性[J].中国科学A辑,2004,34(5):625-640.
[14]胡迪鹤.从P-m链到随机环境中的马氏链[J].数学年刊A辑,2004,25(1):65-78.
[15]李应求.关于马氏环境中马氏链的几点注记[J].数学进展,1999,28(4):358-360.
[16]李应求.随机环境中马氏链与马氏双链间的相互关系[J].数学学报,2006,49(6):1373-1380.
[17]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]SOLOMN F.Random walks in a random environment[J].Ann Probab,1975,3(1):1-31.
[3]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.
[4]ALILI S.Persistent random walks in stationary environment[J].Journal of Statistical Physics,1999,94(3):469-494.
[5]SMITH W L,WILKINSON W E.On branching processes in random environments[J].Ann Math Statist,1969,40(3):814-827.
[6]胡杨利,吴庆平,李应求.随机环境中依赖年龄分枝过程的爆炸问题[J].数学学报A辑,2010,53(5):1027-1034.
[7]COGBURN R.Markov Chains in random environments[J].Ann Probab,1980,8(3):908-916.
[8]COGBURN R.The ergodic theory of Markov chains in random environments[J].Z W,1984,66(2):109-128.
[9]COGBURN R.On direct convergence and periodicity for transition probabilities of Markov chains in random environments[J].Ann Probab,1990,18(2):642-654.
[10]COGBURN R.On the central limit theorem for Markov chains in random environments[J].Ann Probab,1991,19(2):587-604.
[11]OREY S.Markov chains with stochastically stationary transition probabilities[J].Ann Probab,1991,19(3):907-928.
[12]丁万鼎.关于随机环境中的马尔可夫链的马氏性[J].安徽师大学报,1986,(4):1-5.
[13]胡迪鹤.随机环境中q-过程的存在唯一性[J].中国科学A辑,2004,34(5):625-640.
[14]胡迪鹤.从P-m链到随机环境中的马氏链[J].数学年刊A辑,2004,25(1):65-78.
[15]李应求.关于马氏环境中马氏链的几点注记[J].数学进展,1999,28(4):358-360.
[16]李应求.随机环境中马氏链与马氏双链间的相互关系[J].数学学报,2006,49(6):1373-1380.
[17]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.