Central Limit Theorems for Supercritical Superprocesses
Central Limit Theorems for Supercritical Superprocesses
复制标题
DOI：
10.1016/j.spa.2014.09.014
复制
发表时间：
2013-10
影响因子：
1.4
通讯作者：
Yanxia Ren;R. Song;Rui Zhang
中科院分区：
文献类型：
--
作者：
Yanxia Ren;R. Song;Rui Zhang
本文建立了一类具有空间依赖分支机制且满足二阶矩条件的一般超过程的中心极限定理。这个中心极限定理推广和统一了Mirachovich（2012）和Ren等人最近得到的所有中心极限定理。（2014）用于超临界超级Ornstein-Uhlenbeck过程。这个中心极限定理的优点是它允许我们描述极限高斯场。在具有非空间依赖分支机制的超临界超Ornstein-Uhlenbeck过程的情况下，我们的中心极限定理揭示了极限高斯场的更独立的结构。
In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and unifies all the central limit theorems obtained recently in Miłoś (2012) and Ren et al. (2014) for supercritical super Ornstein–Uhlenbeck processes. The advantage of this central limit theorem is that it allows us to characterize the limit Gaussian field. In the case of supercritical super Ornstein–Uhlenbeck processes with non-spatially dependent branching mechanisms, our central limit theorem reveals more independent structures of the limit Gaussian field.