| 关于随机环境中的Galton-Watson分枝过程渐近性质的一个注记 |
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| 引用本文： | 王汉兴,赵飞,卢金余.关于随机环境中的Galton-Watson分枝过程渐近性质的一个注记[J].上海大学学报(英文版),2006,10(2):95-99. |
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| 作者姓名： | 王汉兴 赵飞 卢金余 |
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| 作者单位： | Department of Mathematics and Statistics Shanghai Lixin University of Commerce Shanghai 201620 P.R. China，Department of Mathematics College of Sciences Shanghai University Shanghai 200444 P.R. China，Department of Mathematics College of Sciences Shanghai University Shanghai 200444 P.R. China |
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| 摘 要： | 1Introduction AGalton Watsonbranchingprocessinrandom environments13]isageneralizationofstandardGalton Watsonbranchingprocesses.Itwasfirstformulatedby SmithandWilknson1]inthespecificcasewheretheen vironmentalprocessisi.i.d.randomvariables.The structureof…
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| 关 键 词： | 分支过程 随机环境 消灭概率 Galton-Watson分枝 渐近性质 |
| 文章编号： | 1007-6417（2006）02-0095-05 |
| 收稿时间： | 2004-06-15 |
| 修稿时间： | 2004-12-02 |
A note on asymptotic behavior of Galton-Watson branching processes in random environments |
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| Han-xing Wang Ph. D.,Fei Zhao,Jn-yu Lu.A note on asymptotic behavior of Galton-Watson branching processes in random environments[J].Journal of Shanghai University(English Edition),2006,10(2):95-99. |
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| Authors: | Han-xing Wang Ph D Fei Zhao Jn-yu Lu |
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| Institution: | 1. Department of Mathematics and Statistics, Shanghai Lixin University of Commerce, Shanghai 201620, P.R. China
2. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P.R. China |
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| Abstract: | In this paper, we investigate Galton-Watson branching processes in random environments. In the case where the environmental
process is a Markov chain which is positive recurrent or has a transition matrix Q (θ,α) such that sup,, Q (θ,α) > 0 for some a, we prove that the model has the asymptotic behavior being similar to that of Galton-Watson branching processes.
In other case where the environments are non-stationary independent, the sufficient conditions are obtained for certain extinction
and uncertain extinction for the model. |
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| Keywords: | branching processes random environmental processes extinction probabilities |
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