【摘要】：本文主要研究了經(jīng)典分枝過程的大偏差問題和隨機(jī)環(huán)境中受控分枝過程的極限問題,具體內(nèi)容如下：在第一章中,我們首先介紹了經(jīng)典分枝過程和隨機(jī)環(huán)境中受控分枝過程的研究背景和發(fā)展現(xiàn)狀;其次我們介紹了這兩種過程的定義;最后我們給出了本文的主要結(jié)果.在第二章中,我們研究了上臨界分枝過程中的大偏差問題,分別在p_1=0和p_10兩種情形下得到了(W-W_n)/W_n的大偏差原理.在第三章中,我們討論了隨機(jī)環(huán)境中受控分枝過程的極限問題以及滅絕問題：首先給出了過程{Z_n:n∈N}在{S_n,n≥0}下的規(guī)范化過程{(?)_n：n∈N}幾乎處處收斂,L~1,L~2收斂的充分條件;其次給出了過程{(?)_n：n∈N}的極限非退化的必要條件;然后得到了過程{Z_n:n∈N}在{I_n,n≥0}下的規(guī)范化過程{(?)_n:n∈N}幾乎處處收斂,L1收斂的充分條件;最后給出了平穩(wěn)遍歷環(huán)境下,過程{Z_n}n0的增長率的一個上界以及過程滅絕的充分條件.
[Abstract]:In this paper, the large deviation problem of classical branching process and the limit problem of controlled branching process in random environment are studied. The main contents are as follows: in Chapter 1, Firstly, we introduce the background and development of classical branching processes and controlled branching processes in random environments. Secondly, we introduce the definitions of these two processes, and finally, we give the main results of this paper. In the second chapter, we study the problem of large deviation in the process of upper critical branching. We obtain the large deviation principle of (W-W_n) / Wn in the case of p _ s _ 1 and p _ s _ 10, respectively. In chapter 3, we discuss the limit problem and extinction problem of controlled branching process in random environment: firstly, we give the process {Z_n:n 鈭，

本文編號：2374020