| 随机环境中线性控制分枝链的概率性质 |
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| 引用本文： | 侯传志,陆中胜.随机环境中线性控制分枝链的概率性质[J].南京理工大学学报(自然科学版),2006,30(3):385-388. |
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| 作者姓名： | 侯传志 陆中胜 |
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| 作者单位： | 南京理工大学,理学院,江苏,南京,210094 |
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| 摘 要： | 引进了随机环境中线性控制分枝链的基本概念，讨论了这种概率模型的灭绝概率，用生成母函数严格表达了第n步灭绝的概率，进而讨论了各类母函数之间的关系，并得到了随机环境中线性控制分枝链的期望公式；基于以上的结果，采用鞅方法，严格表达了随机环境中线性控制分枝链的增殖速度。
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| 关 键 词： | 随机环境 线性控制分枝链 生成母函数 鞅 灭绝概率 增殖速度 |
| 文章编号： | 1005-9830（2006）03-0385-04 |
| 收稿时间： | 2004-09-29 |
| 修稿时间： | 2006-04-03 |
Properties of Probability for Linear Controlled Branching Process in Random Environment |
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| HOU Chuan-zhi,LU Zhong-sheng.Properties of Probability for Linear Controlled Branching Process in Random Environment[J].Journal of Nanjing University of Science and Technology(Nature Science),2006,30(3):385-388. |
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| Authors: | HOU Chuan-zhi LU Zhong-sheng |
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| Abstract: | The definition of linear controlled branching process in a random environment is introduced, and the extinction probabilities of the model are studied. The original generating function is used to show the nth extinction probability, and the relations of all kinds of generating functions are studied. The exact formulas of mathematical expectation of the model are produced. Finally, the tool of martingale is used to study the proliferation rate of linear controlled branching process in a random environment. |
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| Keywords: | random environment linear controlled branching process original generating function martingale extinction probabilities proliferation rate |
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