Central Limit Theorems for Supercritical Superprocesses
Abstract
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 Mi{\l}o\'{s} (2012, arXiv:1203:6661) and Ren, Song and Zhang (2013, to appear in Acta Appl. Math., DOI 10.1007/s10440-013-9837-0) 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.
Cite
@article{arxiv.1310.5410,
title = {Central Limit Theorems for Supercritical Superprocesses},
author = {Yan-Xia Ren and Renming Song and Rui Zhang},
journal= {arXiv preprint arXiv:1310.5410},
year = {2014}
}