出生率与年龄段有关的生灭分枝树  

Birth-death branching tree with age-dependent birth-rate

作　　者：王汉兴[1] 傅云斌[2,1] 颜云志[1] 卢桂林[1] 胡细[3] 于娜 

机构地区：[1]上海立信会计学院数学与信息学院,上海201600 [2]上海大学理学院数学系,上海200444 [3]上海工程技术大学,上海201600 [4]上海电力大学,上海201300

出　　处：《中国科学：数学》2013年第4期383-398,共16页Scientia Sinica：Mathematica

基　　金：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);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.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 distri-butions 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.

关 键 词：随机图 生灭过程 分枝树 

分 类 号：O211.6[理学—概率论与数理统计]