分枝过程与随机环境中受控分枝过程的极限定理

发布时间：2018-12-12 05:38

【摘要】：本文主要研究了经典分枝过程的大偏差问题和随机环境中受控分枝过程的极限问题,具体内容如下：在第一章中,我们首先介绍了经典分枝过程和随机环境中受控分枝过程的研究背景和发展现状;其次我们介绍了这两种过程的定义;最后我们给出了本文的主要结果.在第二章中,我们研究了上临界分枝过程中的大偏差问题,分别在p_1=0和p_10两种情形下得到了(W-W_n)/W_n的大偏差原理.在第三章中,我们讨论了随机环境中受控分枝过程的极限问题以及灭绝问题：首先给出了过程{Z_n:n∈N}在{S_n,n≥0}下的规范化过程{(?)_n：n∈N}几乎处处收敛,L~1,L~2收敛的充分条件;其次给出了过程{(?)_n：n∈N}的极限非退化的必要条件;然后得到了过程{Z_n:n∈N}在{I_n,n≥0}下的规范化过程{(?)_n:n∈N}几乎处处收敛,L1收敛的充分条件;最后给出了平稳遍历环境下,过程{Z_n}n0的增长率的一个上界以及过程灭绝的充分条件.
[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，

本文编号：2374020