分枝马氏过程与超过程的中心极限定理

doi:10.3969/j.issn.1000-1565.2021.05.003

摘要/Abstract

摘要： 给出近几年来在分枝马氏过程与超过程的极限理论方面得到的部分结果.主要包括分枝机制满足二阶矩条件的分枝Hunt过程的中心极限定理;分枝机制满足二阶矩条件的一般超过程的中心极限定理;分枝机制是空间齐次的稳定分枝机制的超OU过程的中心极限定理.文章同时涉及到大数律结果.

关键词: 分枝Hunt过程, 超过程, 大数律, 中心极限定理

Abstract: Some results on limit theorems for branching Markov processes and superprocesses that we have- DOI:10.3969/j.issn.1000-1565.2021.05.003分枝马氏过程与超过程的中心极限定理任艳霞¹,宋仁明^2,3(1.北京大学数学科学学院,北京 100871;2.伊利诺伊大学数学系,厄巴纳 G1801;3. 四川大学数学系,四川成都 610065)任艳霞理学博士,1995年毕业于南开大学,现任北京大学数学科学学院教授、北京大学统计科学中心教授.博士生导师,本科、硕士均毕业于河北大学;2000年获得全国优秀博士学位论文奖,主要从事测度值马氏过程及分枝粒子系统的研究,在Ann Probab、Stoch Proc Appl等著名学术期刊发表SCI收录论文60余篇;承担国家自然科学基金、科技部重点研发计划、教育部高等学校博士点基金等多项科研项目.宋仁明理学博士,1993年毕业于美国佛罗里达大学,现任美国伊利诺伊大学数学系教授,博士生导师,本科、硕士均毕业于河北大学,2019年开始任四川大学数学学院长江讲座教授,主要从事马氏过程、概率位势理论、随机分析与分枝过程的研究,在Probab Theory Related Fields、Ann Probab等著名学术期刊发表SCI收录论文140余篇,承担国家自然科学基金重点项目、面上项目、Simons Foundation Grant等多项科研项目.摘要:给出近几年来在分枝马氏过程与超过程的极限理论方面得到的部分结果.主要包括分枝机制满足二阶矩条件的分枝Hunt过程的中心极限定理;分枝机制满足二阶矩条件的一般超过程的中心极限定理;分枝机制是空间齐次的稳定分枝机制的超OU过程的中心极限定理.文章同时涉及到大数律结果.关键词:分枝Hunt过程;超过程;大数律;中心极限定理中图分类号:O211.62 文献标志码:A 文章编号:1000-1565(2021)05-0463-18Central limit theorems for branching Markovprocesses and superprocessesREN Yanxia¹, SONG Renming^2,3(1.School of Mathematical Science,Peking University,Beijing 100871,China;2.Department of Mathematics,University of Illinois,Urbana G1801,United States;3.College of Mathematics,Sichuan University,Chengdu 610065,China)Abstract: Some results on limit theorems for branching Markov processes and superprocesses that we have- 收稿日期:2020-10-15 基金项目:国家自然科研基金资助项目(11931004; 12071011); Simons Foundation Grant(#429343 Renming Song)基金资助项目第一作者:任艳霞(1965—),女,河北石家庄人,北京大学教授,博士生导师,主要从事测度值马氏过程与分枝粒子系统方向研究.E-mail: yxren@math.pku.edu.cn 通信作者:宋仁明(1963—),男,河北邯郸人,美国伊利诺伊大学教授,博士生导师,四川大学教授,主要从事马氏过程、概率位势理论、随机分析与分枝过程的研究.E-mail: rsong@illinois.edu第5期任艳霞等:分枝马氏过程与超过程的中心极限定理obtained in recent years are described. These include central limit theorems for branching Hunt processes with general branching mechanisms having finite second moment, central limit theorems for superprocesses with general branching mechanisms having finite second moment, and central limit theorems for super Ornstein-Uhlenbeck processes with spatially homogeneous branching mechanisms.The law of large numbers are also involved.

Key words: branching hunt process, superprocess, law of large number, central limit theorem

中图分类号:

O211.62

任艳霞,宋仁明. 分枝马氏过程与超过程的中心极限定理[J]. 河北大学学报(自然科学版), 2021, 41(5): 463-480.

REN Yanxia, SONG Renming. Central limit theorems for branching Markov processes and superprocesses[J]. Journal of Hebei University(Natural Science Edition), 2021, 41(5): 463-480.

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