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| 出生率与年龄段有关的生灭分枝树 | |
| 引用本文： | 王汉兴,傅云斌,颜云志,卢桂林,胡细,于娜.出生率与年龄段有关的生灭分枝树[J].中国科学:数学,2013,43(4):383-398. |
| 作者姓名： | 王汉兴 傅云斌 颜云志 卢桂林 胡细 于娜 |
| 作者单位： | 上海立信会计学院数学与信息学院, 上海201600; 上海大学理学院数学系, 上海200444; 上海工程技术大学, 上海201600; 上海电力大学, 上海201300 |
| 基金项目： | 国家自然科学基金(批准号:60872060)、上海市自然科学基金(批准号:12ZR1421000)、上海市教委创新项目基金(批准号:12ZZ193)和国家自然科学青年基金(批准号:11101265)资助项目 |
| 摘 要： | 本文基于生灭过程的生灭演化机理, 将生物繁衍过程描述为有向随机图过程-随机分枝树, 建立了出生率与年龄段有关的生灭分枝树演化模型. 本文研究了任一节点在不同年龄及临死时刻的出度分布、虚出度分布和拟出度分布, 并证明了拟出度过程是随机时刻终止的Poisson过程, 讨论了首生年龄及相对出生年龄的分布, 给出了任一节点成为孤立节点的概率. |
| 关 键 词： | 随机图 生灭过程 分枝树 |
Birth-death branching tree with age-dependent birth-rate |
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| WANG HanXing,FU YunBin,YAN YunZhi,LU GuiLin,HU Xi,YU Na.Birth-death branching tree with age-dependent birth-rate[J].Scientia Sinica Mathemation,2013,43(4):383-398. | |
| Authors: | WANG HanXing FU YunBin YAN YunZhi LU GuiLin HU Xi YU Na |
| Abstract: | Based on the biological reproduction mechanism, the process of biological reproduction is described as an evolution of random directed graph-birth-death branching tree with age-dependent birth rate. The distributions of out-degree, virtual out-degree and quasi-out-degree of a node at any age are studied. It is proved that the quasi out-degree process is a Poisson process to be terminated at a random time. The distributions of the first-production-age and the relative-birth-age of a node are studied. The probability of a node being isolated is obtained. |
| Keywords: | random graph birth-death processes branching tree |
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