Markov随机分枝树节点的年龄结构  

The Age Structure of Nodes in Markov Random Branching Tree

作　　者：王汉兴[1] 杜瑞杰[1,2] 傅云斌[1] 颜云志[1] 

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

出　　处：《数学学报（中文版）》2015年第3期435-446,共12页Acta Mathematica Sinica：Chinese Series

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);上海市教委创新项目(14YZ152;12ZZ193)

摘　　要：研究了子节点到达过程为时齐泊松过程的随机分枝树,主要给出了一些特征量的解析分析:如分枝树中的实节点数和虚节点数,各代节点数,单个实连通分支的节点数;分枝树中处在不同年龄段的实节点数和虚节点数,单个实连通分支中处在不同年龄段的实节点数,各代节点中处在不同年龄段的实节点数;分枝树中适龄生的节点数和实节点数、超龄生的节点数和实节点数.This paper studies the random branching tree,on which child nodes arrival process is time-homogeneous Poisson process,mainly gets analytical analysis of some characteristics:the number of real nodes and the number of virtual nodes in branching tree,the number of each generation in branching tree,the number of real nodes in every connected component;the number of real nodes and the number of virtual nodes in different age interval in whole branching tree,the number of real nodes in different age interval on a single real component,the number of real nodes in different age interval on each generation of branching tree;the number of nodes or real nodes born at suit-age or at overage.

关 键 词：随机图 分枝过程 随机分枝树 年龄结构 

分 类 号：O211.6[理学—概率论与数理统计]