随机环境中具有随机控制函数两性分枝过程的极限性质

作者:宋明珠;吴永锋 刊名:《应用数学》 上传者:王员

【摘要】本文建立随机环境中具有随机控制函数的两性分枝过程,得到该模型概率母函数之间的关系式.当控制函数上可加时,证明配对单元平均增长率的极限是存在的,同时得到配对单元平均增长率一系列的极限性质,进而推进了前人的研究.

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应 用 数 学 MATHEMATICA APPLICATA 2015,28(1):33-40 Limiting Behavior of the Bisexual Galton。-W atson Branching Process with Random Control Functions in Random E nvironments SONG Mingzhu(宋明珠),WU Yongfeng(~永锋) (Department of Mathematics and Computer Science,Tongling University,Tongling 244000,China) Abstract:In this paper,the authors introduce a bisexual Gahon-Watson branching process with random control functions in random environments(BGW PFER),some relations among the probabili— ty generating functions(PGF)with the process are obtained.When BGW PFER and random control functions are superadditive,the existence of the limit of mean growth rate per mating unit is proved。 and limit theorems of mean growth rate per mating unit are established. Key words:Bisexua1 Galton—W atson branching process;Random environment;Ran— dom control function;M ean growth rate per mating unit CLC Number:02l1.65 AMS(2000)Subject Classification:60F37;6oj80 Doeument code:A Article ID:1O01—9847(2015)O1-0033—08 1.Introduction Daley (1 968) introduced the bisexual Galton—W atson branching process (BGW P)as a two—type branching model{(F ,M,*),n一 1,2,⋯)defined recursively: z z 一 N,(F, ,M )一 ( , ),n一 0,1,2,⋯ , i一 1 1一 L(聪 l,M 1),n一 0,1,2,⋯ , where N is a positive integer and the empty sum is considered to be(O,0).Intuitively, and m, represent the number of females and males produced by the ith mating unit in nth genera— tion,{( ,m未 ),i一 1,2,⋯,n一0,1,2,⋯)is a sequence of independent and

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