| 随机环境中的分枝随机游动的若干极限定理 |
| |
| 作者姓名： | 方亮 胡晓予 |
| |
| 作者单位： | 中国科学院研究生院数学科学学院, 北京 100049 |
| |
| 基金项目： | 国家自然科学基金(10871200)资助 |
| |
| 摘 要： | 假设{Zn;n=0,1,2,…}是一个随机环境中的分枝随机游动(即质点在产生后代的过程中,还作直线上随机游动), ξ ={ξ0,ξ1,ξ2,…} 为环境过程. 记Z(n,x)为落在区间(-∞, x]中的第n代质点的个数,fξn(s)=∑j=0∞ pξn(j)sj 为第n代个体的生成函数, mξn=fξn' (1). 证明了在特定条件下,存在随机序列{tn}使得Z(n,tn)(∏i=0n-1mξi)-1均方收敛到一个随机变量.对于依赖于代的分枝随机游动,仍有类似的结论.
|
| 关 键 词： | 分枝过程 随机环境中的分枝随机游动 依赖于代的分枝随机游动 |
| 收稿时间： | 2010-04-12 |
| 修稿时间： | 2010-06-14 |
Some limit theorems on branching random walks in random environments |
| |
| Authors: | FANG Liang HU Xiao-Yu |
| |
| Institution: | School of Mathematics, Graduate University, Chinese Academy of Sciences, Beijing 100049, China |
| |
| Abstract: | Suppose {Zn;n=0,1,2,…} is a branching random walk in the random environment, and ξ ={ξ0,ξ1,ξ2, …} is the environment process. Let Z(n,x) be the number of the nth generation located in the interval (-∞, x], fξn(s)=∑∞j=0 pξn(j)sj be the generating function of the distribution of the particle in the nth generation, and mξn=fξn' (1). We show that under the specific conditions, there exists a sequence of random variables {tn}, so that Z(n,tn)(∏i=0n-1mξi)-1 converges in L2. For branching random walks in varying environments, we have similar results. |
| |
| Keywords: | branching process branching random walks in random environments branching random walks in varying environments |
|
| 点击此处可从《》浏览原始摘要信息 |
| 点击此处可从《》下载免费的PDF全文 |
|
