Functional central limit theorems for supercritical superprocesses

TL;DR

This paper proves functional central limit theorems for a broad class of supercritical superprocesses with spatially dependent branching, extending previous results and providing refined asymptotic behavior insights.

Contribution

It introduces new functional CLTs for supercritical superprocesses with spatial dependence, generalizing prior multitype branching process results.

Findings

Established functional CLTs for supercritical superprocesses

Extended results to spatially dependent branching mechanisms

Refined previous central limit theorems

Abstract

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 underline motion is an irreducible Markov chain on $E$, our results are superprocess analogs of the functional central limit theorems of \cite{Janson} for supercritical multitype branching processes. The results of this paper are refinements of the central limit theorems in \cite{RSZ3}.