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.
Abstract
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
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Key words
random graph /
branching process /
random branching tree /
age structure
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参考文献
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脚注
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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)及上海市教委创新项目(14YZ152,12ZZ193)
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