Central Limit Theorems for Supercritical Branching Markov Processes

TL;DR

This paper proves spatial central limit theorems for a broad class of supercritical branching Markov processes, extending previous results to more general mechanisms and ensuring non-degenerate normal limits.

Contribution

It generalizes existing spatial CLTs for branching processes to include more complex spatial-dependent mechanisms with non-degenerate limits.

Findings

Established spatial CLTs for supercritical branching Markov processes

Extended previous results to more general spatial-dependent mechanisms

Normal limits are non-degenerate in the new theorems

Abstract

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems proved in [1], P. for branching OU processes with binary branching mechanisms. Compared with the results of [1], our central limit theorems are more satisfactory in the sense that the normal random variables in our theorems are non-degenerate.