| 一类分支过程的收敛性 |
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| 引用本文： | 林祥.一类分支过程的收敛性[J].数学物理学报(A辑),2006,26(6):897-905. |
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| 作者姓名： | 林祥 |
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| 作者单位： | 中南大学数学学院概率统计研究所 长沙 |
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| 基金项目： | 国家自然科学基金(10171009)资助 |
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| 摘 要： | 随机稳定性是各种随机模型中的至关重要的问题,随机稳定性中的关键问题是找出过程遍历,指数遍历和强遍历的准则．该文对一类重要的分支过程给出了过程指数遍历及强遍历的条件．在证明中主要应用了几种不同的比较方法,从该文的结果可以看出,这种方法是有效的,因而在其它情形中也是非常有意义的．而且所得结果的概率意义也是十分清楚的．
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| 关 键 词： | 随机稳定性 遍历 指数遍历 强遍历 |
| 文章编号： | 1003-3998（2006）06-897-09 |
| 收稿时间： | 2004-12-29 |
| 修稿时间： | 2006-03-16 |
The Convergence Property of a Type of Branching Processes |
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| Zhang Hanjun,Lin Xiang,Zhang Hanjun.The Convergence Property of a Type of Branching Processes[J].Acta Mathematica Scientia,2006,26(6):897-905. |
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| Authors: | Zhang Hanjun Lin Xiang Zhang Hanjun |
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| Institution: | 1.School of Mathematics, Central South University, Changsha 410075; 2.Discipline of Mathematics, School of Physical Sciences, The University of Queensland, St Lucia, Australia |
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| Abstract: | Stochastic stability is of crucial importance in all kinds of stochastic models. Such investigation involves finding criteria ergodicity, exponential ergodicity and strong ergodicity. This paper is devoted to studing an important class of time-continuous branching processes. Exponential ergodicity and strong ergodicity criteria for the processes are presented. Several different comparison methods are used in our proofs. The resulting shows that the method is effective and hence should be meaningful in other situations. Moreover, the probability meaning of our results is clear. |
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| Keywords: | Stochastic stability Ergodicity Exponential ergodicity Strong ergodicity |
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