本文關(guān)鍵詞： 分支過程 可分解 臨界 極限理論 條件概率　出處：《南京大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：分支過程應(yīng)用十分廣泛,是隨機(jī)過程的重要分支。本文對可分解分支過程理論做了簡單的介紹,包括經(jīng)典的Galton-Watson,可分解的定義,母函數(shù),滅絕概率等。文章著重研究了在臨界狀態(tài)下,粒子的滅絕速度,以及概率母函數(shù)的極限行為。眾所周知,臨界狀態(tài)的分支過程滅絕概率q=1。我們假設(shè)n時(shí)刻滅絕,研究滅絕時(shí)刻的概率。本文還并進(jìn)一步研究了粒子數(shù)目的條件期望。
[Abstract]:Branching process is widely used and is an important branch of stochastic process. In this paper, the theory of decomposable branching process is briefly introduced, including the classical Galton-Watson, the definition of decomposable process. In this paper, the extinction rate of particles in critical state and the limit behavior of probabilistic parent function are studied. The extinction probability of the critical state in the branching process Q ~ (1). We assume the extinction at n moment and study the extinction probability at the time of extinction. We also study the conditional expectation of the number of particles in this paper.
【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
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本文編號：1470485