| 以0为飞射壁的生灭过程爆发前的若干性质 |
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| 引用本文： | 朱全新,戴永隆.以0为飞射壁的生灭过程爆发前的若干性质[J].数学物理学报(A辑),2007,27(3):456-469. |
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| 作者姓名： | 朱全新 戴永隆 |
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| 作者单位： | 华南师范大学数学系，中山大学数学系 广州 510631，广州 510275 |
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| 基金项目： | 国家自然科学基金;广东省自然科学基金 |
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| 摘 要： | 该文首次研究以0为飞射壁的生灭过程爆发前的若干性质, 通过引入线性方程组和推移算子,得到了多种情况下此类过程在爆发前从状态 i 出发运动到状态 n(i ≤ n ≤∞ 或 n≤ i)的概率和平均时间的精确表达式.同时,我们还定义了mi,ei,Ni,R 等一系列特征数, 并表明了这些特征数的概率意义.
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| 关 键 词： | Qa0过程 生灭过程 飞射壁 爆发前 |
| 文章编号： | 1003-3998（2007）03-456-14 |
| 收稿时间： | 2004-05-14 |
| 修稿时间： | 2004-05-142006-01-08 |
Properties of the Birth and Death Processes with Zero as Their Leap-reflecting Barriers before Explosion |
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| Zhu Quanxin,Dai Yonglong.Properties of the Birth and Death Processes with Zero as Their Leap-reflecting Barriers before Explosion[J].Acta Mathematica Scientia,2007,27(3):456-469. |
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| Authors: | Zhu Quanxin Dai Yonglong |
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| Institution: | 1.Department of Mathematics, South China Normal University, Guangzhou 510631;2.Department of Mathematics, Zhongshan University, Guangzhou 510275 |
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| Abstract: | This paper first deals with some properties of birth and death processes with state 0 as their leap-reflecting barriers before explosion. By proposinga system of linear equations and shift operator, the authors obtain some precise expressions of both probability and average time when the processes move from state i to state n(i ≤ n ≤∞ or n≤ i) in several cases. On the otherhand, the authors not only give a new definition of the characteristic numberssuch as mi,ei,Ni,R etc, but also show their probability meanings. |
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| Keywords: | Q_0~a process Birth and death process Leap-reflecting barrier Before explosion |
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