Central limit theorems for supercritical superprocesses with immigration

TL;DR

This paper proves a central limit theorem for a broad class of supercritical superprocesses with immigration, extending previous results and including spatially dependent branching mechanisms under second moment conditions.

Contribution

It introduces a law of large numbers for supercritical superprocesses with immigration and establishes a generalized central limit theorem for these processes.

Findings

Law of large numbers for superprocesses with immigration

Central limit theorem extending previous results

Applicable to spatially dependent branching mechanisms

Abstract

In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with immigration with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem extends and generalizes the results obtained by Ren, Song and Zhang[2015]. We first give law of large numbers for supercritical superprocesses with immigration since there is few convergence result on immigration superprocesses, then based on these results, we establish the central limit theorem.