下临界多物种带移民分支过程的若干极限问题
发布时间：2019-02-15 00:48
【摘要】：本文主要对多物种GW分支过程及多物种带移民分支过程的一些经典结论进行了拓展。首先,对下临界GW分支过程引入了初始时刻粒子数目向量的概率分布—Poisson分布,讨论了在下临界情形下Poisson分布的参数λ随代际数n以特定方式增大时的极限概率分布。然后,在多物种带移民分支过程中,提出了系统中最初时刻存在的粒子的后代未灭绝的情况,并推导出此情况下的条件极限概率分布;以及在原本地粒子后代恰好灭绝时,系统中粒子总数向量的期望;最后,拓展了下临界单物种带移民分支过程关于前n代粒子总数的相关结论到多物种带移民分支过程。其一为前n代粒子总数的母函数的表达式;其二为下临界情形下前n代粒子总数与代际数n同阶的事实。
[Abstract]:In this paper, some classical conclusions about GW branching process and migration process with multi-species are extended. Firstly, the probability distribution of the initial particle number vector, Poisson distribution, is introduced for the lower critical GW bifurcation process. The limit probability distribution of the parameter 位 of the Poisson distribution under the lower critical condition is discussed when the parameter 位 increases in a specific manner with the intergenerational number n. Then, in the process of multi-species migration branch, the condition that the offspring of the particles that existed at the initial time of the system is not extinct is proposed, and the conditional limit probability distribution in this case is deduced. And the expectation of the particle total vector in the system when the progeny of the original particle is extinct. Finally, we extend the conclusion of the lower critical single species migration branching process on the number of the previous n-generation particles to the multi-species migration branching process. The first is the expression of the generating function of the total number of the previous n-generation particles, the other is the fact that the total number of the previous n-generation particles is of the same order as the intergenerational number in the case of lower critical condition.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.65
，
本文编号：2422778
[Abstract]:In this paper, some classical conclusions about GW branching process and migration process with multi-species are extended. Firstly, the probability distribution of the initial particle number vector, Poisson distribution, is introduced for the lower critical GW bifurcation process. The limit probability distribution of the parameter 位 of the Poisson distribution under the lower critical condition is discussed when the parameter 位 increases in a specific manner with the intergenerational number n. Then, in the process of multi-species migration branch, the condition that the offspring of the particles that existed at the initial time of the system is not extinct is proposed, and the conditional limit probability distribution in this case is deduced. And the expectation of the particle total vector in the system when the progeny of the original particle is extinct. Finally, we extend the conclusion of the lower critical single species migration branching process on the number of the previous n-generation particles to the multi-species migration branching process. The first is the expression of the generating function of the total number of the previous n-generation particles, the other is the fact that the total number of the previous n-generation particles is of the same order as the intergenerational number in the case of lower critical condition.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.65
，
本文编号：2422778
本文链接：https://www.wllwen.com/kejilunwen/yysx/2422778.html
