| THE ERGODICITY FOR BI-IMMIGRATION BIRTH AND DEATH PROCESSES IN RANDOM ENVIRONMENT |
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| 作者姓名： | 胡迪鹤 张书林 |
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| 作者单位： | [1]School of Mathematics and Statistics, Yunnan University, Kunming 650091, China [2]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China [3]Department of Mathematics, Hong Kong Baptist University, Hong Kong, China |
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| 基金项目： | Supported by the NNSF of China （10371092, 10771185） and the Foundation of Whuan University |
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| 摘 要： | The concepts of bi-immigration birth and death density matrix in random environment and bi-immigration birth and death process in random environment are introduced. For any bi-immigration birth and death matrix in random environment Q（θ） with birth rate λ 〈 death rate μ, the following results are proved, （1） there is an unique q-process in random environment, P^-（θ＊（0）;t） = （p^-（θ^＊（0）;t,i,j）,i,j ≥ 0）, which is ergodic, that is, lim t→∞（θ^＊（0）;t,i,j） = π^-（θ^＊（0）;j） ≥0 does not depend on i ≥ 0 and ∑j≥0π （θ＊（0）;j） = 1, （2） there is a bi-immigration birth and death process in random enjvironment （X^＊ = {X^＊,t ≥ 0},ε^＊ = {εt,t ∈ （-∞, ∞）}） with random transition matrix P^-（θ^＊ （0）;t） such that X^＊ is a strictly stationary process.
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| 关 键 词： | 随机环境 矩阵 数学分析 求解方法 |
| 收稿时间： | 2005-06-21 |
| 修稿时间： | 2005-12-05 |
The Ergodicity for Bi-Immigration Birth and Death Processes in Random Environment |
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| Hu Dihe,Zhang Shulin,.THE ERGODICITY FOR BI-IMMIGRATION BIRTH AND DEATH PROCESSES IN RANDOM ENVIRONMENT[J].Acta Mathematica Scientia,2008,28(1):43-53. |
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| Authors: | Hu Dihe Zhang Shulin |
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| Affiliation: | aSchool of Mathematics and Statistics, Yunnan University, Kunming 650091, China School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;bDepartment of Mathematics, Hong Kong Baptist University, Hong Kong, China |
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| Abstract: | Density matrix in random environment, random transition matrix, Markov process in random environment, bi-immigration birth and death density matrix in random environment, bi-immigration birth and death process in random environment |
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| Keywords: | Density matrix in random environment random transition matrix Markov process in random environment bi-immigration birth and death density matrix in random environment bi-immigration birth and death process in random environment |
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