报告题目：Limit theorems for a supercritical two-type decomposable branching process in a random environment

主 讲 人：王艳清教授 （中南财经政法大学）

报告时间：4月9日（周三）上午9:00-10:00

腾讯会议：392-916-522

报告摘要：Let $Z_n=(Z_n^{(1)},Z_n^{(2)})$ be a two-type decomposable branching process in an independent and identically distributed random environment, where a type $1$ particle may produce particles of types 1 and 2, while a type 2 particle can only give birth to type 2 particles. We consider asymptotic properties of this process in the supercritical case. Because $Z_n^{(1)}$ is an usual single-type branching process in a random environment, we only consider $Z_n^{(2)}$. First, under some moment conditions, we find a suitable factor $\Pi_n$ such that the normalized population size $W_n=\frac{Z_n^{(2)}}{\Pi_n}$ converges almost surely to a finite random variable $W$, and provide a decomposition expression and a non-degeneracy condition of $W$. Second, we give conditions under which $(W_n)$ is convergent in $L^p$ for $p\geq1$, and bounded in $L^p$ for $0<p<1$. Finally, we establish a central limit theorem for $\log Z_n^{(2)}$.

报告人简介：王艳清，中南财经政法大学统计与数学学院副院长，教授、博导，全国工业统计教学研究会理事，中国现场统计研究会经济与金融分会理事，中国现场统计研究会旅游大数据分会理事。长期从事概率论与数理统计、经济统计相关领域的研究。主持国家自然科学基金、教育部人文社科项目、国家统计局等纵横向课题30余项，在《Electronic Journal of Probability》、《Statistics & Probability Letters》、《中国科学：数学》、《数学学报》、《数理统计与管理》等国内外期刊发表论文20余篇。