一胎多子的生灭分枝树  

Birth-Death Branching Tree with Nodes Being Multiparous

作　　者：王佳元[1] 傅云斌[1,2] 

机构地区：[1]上海大学理学院,上海200444 [2]上海立信会计学院,上海201620

出　　处：《上海大学学报（自然科学版）》2014年第6期749-756,共8页Journal of Shanghai University:Natural Science Edition

基　　金：国家自然科学基金资助项目(60872060);上海市自然科学基金资助项目(12ZR1421000);上海市教委创新基金资助项目(12ZZ193;14YZ152)

摘　　要：马氏生灭分枝树模型假定节点每次分娩当且仅当生产1个子节点.假定节点每次分娩的产子数是一随机变量的基础上建立了一胎多子的生灭分枝树演化模型,给出模型的存在性证明,并研究生灭分枝树在不同时刻活着和死亡的节点数、连通分支的个数、任一节点在活着的条件下在不同年龄的子节点数、任一节点在临死前的子节点数.It is assumed that only one son-node is born in each delivery in the model of Markov birth-death branching tree.This paper assumed that the number of son-nodes born in each delivery is a random variable,and develop a model of birth-death branching tree with nodes being multiparous.Existence of this model is shown.We study the numbers of living nodes,dead nodes,connected components,son-nodes of any node at any age,and son-nodes at dying moment.

关 键 词：随机图 分枝过程 生灭分枝树 马氏过程 

分 类 号：O211.62[理学—概率论与数理统计]