下临界多物种分支过程后代总人口数生成函数  

THE GENERATING FUNCTION OF TOTAL PROGENY IN A SUBCRITICAL MULTI-TYPE BRANCHING PROCESS

作　　者：张美娟[1] 

机构地区：[1]北京师范大学数学科学学院 数学与复杂系统教育部重点实验室,北京100875

出　　处：《北京师范大学学报（自然科学版）》2012年第3期221-224,共4页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10721091)

摘　　要：讨论下临界多物种分支过程后代总人口数的生成函数.通过推导出的下临界多物种分支过程前n代总人口数生成函数Rn(s)的递归公式,利用其单调性得到Rn(s)的极限生成函数ρ(s)为方程t=s*f(t)的解.又ρ(s)即为下临界多物种分支过程后代总人口数的概率生成函数,故有下临界多物种分支过程后代总人口数的概率生成函数为方程t=s*f(t)的解.The generating function of total progeny in a sub-critical multi-type branching process was discussed.Recursion formula for generating function of total number of descendants up to and including the nth generation were deduced and the ancestor was denoted Rn（s）.By monotonicity of Rn（s）,it was derived that the limit ρ（s） was a solution of equation t=s＊f（t）.It was further found that ρ（s） was generation function of total progeny.It was concluded that generating function of total progeny in a sub-critical multi-type branching process was the solution of equation t=s＊f（t）.

关 键 词：多物种分支过程 后代总人口数 递归公式 极限生成函数 

分 类 号：O211.63[理学—概率论与数理统计]