Law of Large Numbers for Branching Symmetric Hunt Processes with Measure-Valued Branching Rates

被引：9

作者：

Chen, Zhen-Qing ^{[1
]}

Ren, Yan-Xia ^{[2
,3
]}

Yang, Ting ^{[4
,5
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Peking Univ, LMAM Sch Math Sci, Beijing 100871, Peoples R China

[3] Peking Univ, Ctr Stat Sci, Beijing 100871, Peoples R China

[4] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[5] Beijing Key Lab MCAACI, Beijing 100081, Peoples R China

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2017年 / 30卷 / 03期

关键词：

Law of large numbers; Branching Hunt processes; Spine approach; h-transform; Spectral gap; MARKOV-PROCESSES; LIMIT-THEOREMS; DIRICHLET FORMS; GREEN-FUNCTIONS; DIFFUSIONS; SUPERDIFFUSIONS; PERTURBATION;

D O I：

10.1007/s10959-016-0671-y

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We establish weak and strong laws of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the branching mechanism being general and state dependent. Our work is motivated by recent work on the strong law of large numbers for branching symmetric Markov processes by Chen and Shiozawa (J Funct Anal 250:374-399, 2007) and for branching diffusions by Englander et al. (Ann Inst Henri Poincar, Probab Stat 46:279-298, 2010). Our results can be applied to some interesting examples that are covered by neither of these papers.

引用

页码：898 / 931

页数：34

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