Central limit theorems for supercritical branching Markov processes

被引：14

作者：

Ren, Yan-Xia ^{[1
,2
]}

Song, Renming ^{[3
]}

Zhang, Rui ^{[1
]}

机构：

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

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

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 266卷 / 03期

关键词：

Central limit theorem; Branching Markov process; Supercritical; Martingale; Eigenfunction expansion; OCCUPATION TIME FLUCTUATIONS; LARGE NUMBERS; STRONG LAW; SYSTEMS; ULTRACONTRACTIVITY; CONVERGENCE;

D O I：

10.1016/j.jfa.2013.10.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems proved in [1] for branching OU processes with binary branching mechanisms. Compared with the results of [1], our central limit theorems are more satisfactory in the sense that the normal random variables in our theorems are non-degenerate. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：1716 / 1756

页数：41

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