一胎多子的生灭分枝

王佳元1, 傅云斌1, 2

doi:10.3969/j.issn.1007-2861.2014.01.010

上海大学学报(自然科学版) >

2014 , Vol. 20 >Issue 6: 749 - 756

DOI: https://doi.org/10.3969/j.issn.1007-2861.2014.01.010

数理化科学

一胎多子的生灭分枝

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1.上海大学理学院，上海 200444；2.上海立信会计学院，上海 201620

收稿日期: 2013-10-10

网络出版日期: 2014-12-23

基金资助

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）

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Birth-Death Branching Tree with Nodes Being Multiparous

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1. College of Sciences, Shanghai University, Shanghai 200444, China;2. Shanghai Lixin University of Commerce, Shanghai 201620, China

Received date: 2013-10-10

Online published: 2014-12-23

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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，给出了模型的存在性证明，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

关键词： 分枝过程; 马氏过程; 生灭分枝数; 随即图

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王佳元1, 傅云斌1, 2 . 一胎多子的生灭分枝[J]. 上海大学学报(自然科学版), 2014 , 20(6) : 749 -756 . DOI: 10.3969/j.issn.1007-2861.2014.01.010

Abstract

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.

Key words： birth-death branching tree; branching process; Markov process; random graph

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