An application of the backbone decomposition to supercritical super-Brownian motion with a barrier

TL;DR

This paper applies the backbone decomposition technique to analyze the behavior of supercritical super-Brownian motion with a barrier, providing insights into growth, analytical properties, and mass distribution.

Contribution

It introduces a novel application of the backbone decomposition to super-Brownian motion with barriers, connecting existing results to derive new conclusions.

Findings

Growth rate of the rightmost support point

Analytical properties of the FKPP equation

Distribution of mass on the exit measure

Abstract

We analyse the behaviour of supercritical super-Brownian motion with a barrier through the pathwise backbone embedding of Berestycki et al. (2011). In particular, by considering existing results for branching Brownian motion due to Harris et al. (2006) and Maillard [arxiv:1004.1426], we obtain, with relative ease, conclusions regarding the growth in the right most point in the support, analytical properties of the associated one-sided FKPP equation as well as the distribution of mass on the exit measure associated with the barrier.