【摘要】：本文主要對(duì)多物種GW分支過(guò)程及多物種帶移民分支過(guò)程的一些經(jīng)典結(jié)論進(jìn)行了拓展。首先,對(duì)下臨界GW分支過(guò)程引入了初始時(shí)刻粒子數(shù)目向量的概率分布—Poisson分布,討論了在下臨界情形下Poisson分布的參數(shù)λ隨代際數(shù)n以特定方式增大時(shí)的極限概率分布。然后,在多物種帶移民分支過(guò)程中,提出了系統(tǒng)中最初時(shí)刻存在的粒子的后代未滅絕的情況,并推導(dǎo)出此情況下的條件極限概率分布;以及在原本地粒子后代恰好滅絕時(shí),系統(tǒng)中粒子總數(shù)向量的期望;最后,拓展了下臨界單物種帶移民分支過(guò)程關(guān)于前n代粒子總數(shù)的相關(guān)結(jié)論到多物種帶移民分支過(guò)程。其一為前n代粒子總數(shù)的母函數(shù)的表達(dá)式;其二為下臨界情形下前n代粒子總數(shù)與代際數(shù)n同階的事實(shí)。
[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.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O211.65
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本文編號(hào)：2422778