Functional Central Limit Theorems for Supercritical Superprocesses

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• 作者：Yan-Xia Ren ; Renming Song ; Rui Zhang
• 关键词：Functional central limit theorem ; Supercritical superprocess ; Excursion measures of superprocesses
• 刊名：Acta Applicandae Mathematicae
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：147
• 期：1
• 页码：137-175
• 全文大小：
• 刊物主题：Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9036
• 卷排序：147

文摘

In this paper, we establish some functional central limit theorems for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. In the particular case when the state \(E\) is a finite set and the underlying motion is an irreducible Markov chain on \(E\), our results are superprocess analogs of the functional central limit theorems of Janson (Stoch. Process. Appl. 110:177–245, 2004) for supercritical multitype branching processes. The results of this paper are refinements of the central limit theorems in Ren et al. (Stoch. Process. Appl. 125:428–457, 2015).