主题：The rates of convergence of the branching process
主讲人：李应求 长沙理工大学
主持人：姜云卢 威尼斯欢迎你welcome
时间：2023年5月19日（周五）上午10:30-11:30
地点：威尼斯欢迎你welcome石牌校区威尼斯欢迎你welcome大楼（中惠楼）102室
摘要
In this report, we will first introduce some current studies on the convergence rates of branching processes of various types, focusing on our recent work on the convergence rates of branching processes with immigration in a random environment.
For a supercritical branching process $(Z_{n})$ with immigration $(Y_{n})$ in a stationary and ergodic environment $\xi,$ we are interested in the convergence rates of the submartingale $W_{n} =\frac{Z_{n}}{\Pi_{n}}$ to its limit ${W},$ where $(\Pi_{n})$ is an usually used norming sequence.
we study the exponential and geometric convergence rates of $(W_{n})$ a.s. convergence to its limit $W$, similar conclusions hold for the varying environment case; Under suitable conditions, we establish the following central limit theorems and results about the rates of convergence in probability or in law; We obtained a necessary condition and a sufficient condition for the quenched $L^{p}$ $(p > 1)$ convergence of $(W_{n})$, and the exponential convergence rates, Similar results are also hold in a varying environment case.
%we obtained the convergence of $L^{p}$ and it's for the branching process with immigration in a random environment, similar conclusions hold for the varying environment case.
In addition, some preliminary attempts on the convergence rate of the bisexual branching process are introduced. We studied almost sure convergence rates and $L^{p}$ convergence for bisexual branching processes.
主讲人简介
李应求，长沙理工大学数学与统计学院二级教授，博士生导师。李教授一直从事概率统计及其应用研究,主持承担国家自然科学基金项目8项(含1项国际合作项目)、湖南省杰出青年(中青年科技)基金等省部级项目30余项,与浙江大学、武汉大学联合承担国家自然科学基金重点项目1项,发表学术论文100余篇,出版专著1本。
李教授担任中国统计教育学会理事,湖南省经济数学研究会副理事长,湖南省数量经济学会副理事长,湖南省数学会常务理事,湖南欧美同学会、湖南留学人员联合会理事。李教授是长沙理工大学应用统计国家一流建设本科专业负责人、数学湖南省“十二五”重点学科带头人，湖南省新世纪121人才工程第一层次人选,湖南省优秀中青年专家,电力工业部优秀教师,国务院政府特殊津贴专家。李教授获教育部科技进步一等奖、湖南省自然科学二等奖、中华电力教育基金中青年学术带头人二等奖、第一届中国电机工程青年科技奖、第二届湖南省青年科技奖、湖南省科学技术进步三等奖、湖南省教学成果三等奖。
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校对|王国长
责编|麦嘉杰
初审|黄振
审核|郑贤
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