本文選題：小值概率 + 上臨界多物種分支過程��； 參考：《南京大學(xué)》2017年碩士論文

【摘要】：分支過程的小值概率是隨機(jī)過程的極限性質(zhì)研究的一個(gè)重要課題。而小值概率收斂到0的速率則和其分支機(jī)制是密切相關(guān)的,通常分為Schr(?)der case和B(?)ttcher case兩種情況。在單物種的分支過程里,Schr(?)der case和B(?)ttcher case的分類由產(chǎn)生一個(gè)后代的概率決定。本文考慮的是上臨界的多物種分支過程的小值概率問題。根據(jù)Jones(2004)[20]的結(jié)論,上臨界的多物種分支過程的小值概率也是由分支機(jī)制所決定的。不過與單物種的分支過程比較起來,其Schr(?)der case和B(?)ttcher case的定義要復(fù)雜的多。從[20]關(guān)于Schr(?)der case和B(?)ttcher case的定義出發(fā),我們對于兩物種的分支過程得出更加具體的分類條件:可以從后代分布出發(fā)直接判斷分支過程屬于Schr(?)der case,還是B(?)ttcher case。我們從[20]定義里的判斷矩陣A和最小后代矩陣B的譜半徑與冪方收斂性出發(fā),得到了兩物種分支過程分類的充分條件,同時(shí)還得到了一些有趣的結(jié)論,如存在既不是Schr(?)der case也不是B(?)ttcher case的情況。此外,我們推廣了文獻(xiàn)Moters和Ortgiese[30]給出的概率方法,并給出上臨界的多物種分支過程在B(?)ttcher case的小值概率上下界的一個(gè)證明。
[Abstract]:The probability of small value of branching process is an important subject in the study of the limit property of stochastic process. However, the rate of probability converging to zero is closely related to its branching mechanism, which is usually divided into two cases: Schr(?)der case and B(?)ttcher case. The classification of case and B(?)ttcher case in the branching process of a single species is determined by the probability of producing a progeny. In this paper, we consider the small probability problem of the upper critical multispecies branching process. According to the conclusion of Jones-2004 [20], the probability of small value of the upper critical multi-species branching process is also determined by the branching mechanism. But the definition of Schr(?)der case and B(?)ttcher case is much more complex than the branching process of a single species. Based on the definitions of Schr(?)der case and B(?)ttcher case in [20], we obtain more specific classification conditions for the branching processes of the two species: we can directly judge whether the branching processes belong to Schr(?)der case or B(?)ttcher case from the distribution of offspring. Starting from the spectral radius and power square convergence of the judgment matrix A and the minimal descendant matrix B in the definition of [20], we obtain sufficient conditions for the classification of the two species branching processes, and obtain some interesting conclusions at the same time. If there is neither Schr(?)der case nor B(?)ttcher case. In addition, we generalize the probabilistic methods given by Moters and Ortgiese [30], and give a proof of the upper lower bound of the lower probability of the upper critical multispecies branching process in B(?)ttcher case.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O211.65
，

本文編號：1876738