分枝马氏过程与超过程的中心极限定理  

Central limit theorems for branching Markov processes and superprocesses

作　　者：任艳霞[1] 宋仁明 REN Yanxia;SONG Renming(School of Mathematical Science,Peking University,Beijing 100871,China;Department of Mathematics,University of Illinois,Urbana G1801,United States;College of Mathematics,Sichuan University,Chengdu 610065,China)

机构地区：[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

出　　处：《河北大学学报（自然科学版）》2021年第5期463-480,共18页Journal of Hebei University(Natural Science Edition)

基　　金：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。

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.Some results on limit theorems for branching Markov processes and superprocesses that we have 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.

关 键 词：分枝Hunt过程 超过程 大数律 中心极限定理 

分 类 号：O211.62[理学—概率论与数理统计]