期刊论文

Limit Theorems for Controlled Branching Processes in Random Environments

中文

数学学报：中文版

0583-1431

2018

61

2

317-326

10.3969/j.issn.0583-1431.2018.02.011

11571052:国家自然科学基金 2017JJ2271:湖南省自然科学基金 2017JJ2274:湖南省自然科学基金 CX2017SS24:长沙理工大学研究生科研创新项目

本校为第一机构

讨论了随机环境中受控分枝过程$\left\{ {{Z_n}:n \in \mathbb{N}} \right\}$的极限问题.给出了过程在$\left\{ {{S_n}:n \in \mathbb{N}} \right\}$下的规范化过程$\left\{ {{{\hat W}_n}:n \in \mathbb{N}} \right\}$几乎处处收敛、${L^1}$收敛和${L^2}$收敛的充分条件,以及过程$\left\{ {{{\hat W}_n}:n \in \mathbb{N}} \right\}$的极限非退化于0的充分条件和必要条件,得到了过程在$\left\{ {{I_n}:n \in \mathbb{N}} \right\}$下的规范化过程$\left\{ {{{\bar W}_n}:n \in \mathbb{N}} \right\}$几乎处处收敛和${L^1}$收敛的充分条件.

The limiting behaviors for controlled branching processes in random environments are discussed. Under the normalization factor $\left\{ {{S_n}:n \in \mathbb{N}} \right\}$, the normalization processes $\left\{ {{{\hat W}_n}:n \in \mathbb{N}} \right\}$ of are studied, and the sufficient conditions of $\left\{ {{{\hat W}_n}:n \in \mathbb{N}} \right\}$ a.s., ${L^1}$ and ${L^2}$ convergence are given; A sufficient condition and a necessary condition for convergence to a non-degenerate at 0 random variable are got; Under the normalization factor $\left\{ {{I_n}:n \in \mathbb{N}} \right\}$, the norma...