一类右半直线上独立同分布随机环境中的随机游动
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摘要
本文给出在0点以一定概率吸收和反射的右半直线上独立同分布的随机环境中的随机游动模型,讨论了模型的常返性和极限性质,计算了模型的吸收概率.
In this paper, a random walk model that is absorbed and reflected by a certain probability at 0 in independent and identically distributed random environment on the right half-line is given. The recurrence and limit properties of the model are discussed and the absorbing probabilities are calculated.
In this paper, a random walk model that is absorbed and reflected by a certain probability at 0 in independent and identically distributed random environment on the right half-line is given. The recurrence and limit properties of the model are discussed and the absorbing probabilities are calculated.
引文
[1] Kozlov M V. Random walk in a one dimensional random medium [J]. Theor Prob Appl, 1973, 18: 387.
[2] Solomon F. Random walk in a random environment [J]. Ann Prob, 1975, 3: 1.
[3] Karlin S, Taylor H M. A first course in stochastic processes [M]. New York: Academic Press, 1975.
[4] Cogburn R. Markov chains in random environments: the case of Markov environments [J]. Ann Prob, 1980, 8: 908.
[5] Cogburn R. The Ergodic Theory of Markov chains in random environments [J]. Z Wahrach Verw Gebiete, 1984, 66: 109.
[6] Cogburn R. On direct convergence and periodicity for transition probabilities of Markov chains in random environments [J]. Ann Prob, 1990, 18: 642.
[7] 刘磊, 吴芝明, 林涛, 刘大瑞. 基于马尔科夫模型的移动设备链接预测研究[J]. 四川大学学报; 自然科学版, 2015, 52: 45.
[8] 王华明. 一类随机环境中随机游动的值域问题[J]. 中国科学, 2017, 47: 841.
[9] 任敏, 张光辉. 右半直线上依分布收敛独立随机环境中的生灭过程的常返性[J]. 数学学报, 2017, 60: 531.
[10] 胡学平, 李会葆. 直线上随机环境中可逗留的随机游动的若干性质[J]. 数学研究, 2006, 39: 198.
[11] 毕秋香. 半直线上随机环境中随机游动的若干性质[J]. 应用概率统计, 1997, 13: 120.
[12] 任敏, 张光辉. 右半直线上依分布收敛独立随机环境中随机游动的吸收概率[J]. 山东大学学报: 理学版, 2013, 48: 93.
[2] Solomon F. Random walk in a random environment [J]. Ann Prob, 1975, 3: 1.
[3] Karlin S, Taylor H M. A first course in stochastic processes [M]. New York: Academic Press, 1975.
[4] Cogburn R. Markov chains in random environments: the case of Markov environments [J]. Ann Prob, 1980, 8: 908.
[5] Cogburn R. The Ergodic Theory of Markov chains in random environments [J]. Z Wahrach Verw Gebiete, 1984, 66: 109.
[6] Cogburn R. On direct convergence and periodicity for transition probabilities of Markov chains in random environments [J]. Ann Prob, 1990, 18: 642.
[7] 刘磊, 吴芝明, 林涛, 刘大瑞. 基于马尔科夫模型的移动设备链接预测研究[J]. 四川大学学报; 自然科学版, 2015, 52: 45.
[8] 王华明. 一类随机环境中随机游动的值域问题[J]. 中国科学, 2017, 47: 841.
[9] 任敏, 张光辉. 右半直线上依分布收敛独立随机环境中的生灭过程的常返性[J]. 数学学报, 2017, 60: 531.
[10] 胡学平, 李会葆. 直线上随机环境中可逗留的随机游动的若干性质[J]. 数学研究, 2006, 39: 198.
[11] 毕秋香. 半直线上随机环境中随机游动的若干性质[J]. 应用概率统计, 1997, 13: 120.
[12] 任敏, 张光辉. 右半直线上依分布收敛独立随机环境中随机游动的吸收概率[J]. 山东大学学报: 理学版, 2013, 48: 93.