| 随机环境中马氏过程的强遍历性及收敛速度 |
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| 引用本文： | 吕平,胡迪鹤.随机环境中马氏过程的强遍历性及收敛速度[J].杭州师范学院学报(自然科学版),2009,8(2):81-86. |
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| 作者姓名： | 吕平 胡迪鹤 |
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| 作者单位： | 1. 杭州师范大学,理学院,浙江,杭州,310036
2. 云南大学,数学与统计学院,云南,昆明,650091 |
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| 基金项目： | 国家自然科学基金项目，杭州师范大学青年基金项目 |
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| 摘 要： | 文章引进随机环境中马氏过程的模型，研究了该模型的马氏过程满足强遍历性的各种充要条件；证明了当随机转移函数P（θ^·s，s＋t）；x，A）属于G^＋时，强遍历性蕴含了收敛的指数速度；找出了最佳收敛速度；并得到了达到最佳收敛速度的条件．
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| 关 键 词： | 谱半径 随机转移函数 强遍历 右强遍历 一致强遍历 一致右强遍历 |
The Strong Ergodic Principle and Rates of Convergence for Markov Processes with Random Environment |
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| LV Ping,HU Di-he.The Strong Ergodic Principle and Rates of Convergence for Markov Processes with Random Environment[J].Journal of Hangzhou Teachers College(Natural Science),2009,8(2):81-86. |
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| Authors: | LV Ping HU Di-he |
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| Institution: | 1. College of Science, Hangzhou Normal University, Hangzhou 310036, China; 2.School of Mathematics and Statistics, Yunnan University, Kunming 310036, China) |
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| Abstract: | The paper introduces the model of Markov processes in random environments, studies the necessary and sufficient conditions for strong ergodic principles under this model. Moreover, it proves the strong ergodic principle includes the rates of convergence when the random transition function belongs to G^＋. It also finds the best rate of convergence and gets the condition for reaching the best rate of convergence. |
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| Keywords: | spectral radius random transition function strong ergodic right strong ergodic uniformly strong ergodic uniformly right strong ergodic |
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