On the subcritical self-catalytic branching Brownian motions

TL;DR

This paper introduces subcritical self-catalytic branching Brownian motions, constructs these processes with infinite initial particles, and analyzes their coming down from infinity behavior.

Contribution

It extends classical branching Brownian motions by incorporating pairwise catalysis and provides a construction for the subcritical case with infinite initial particles.

Findings

Constructed the subcritical SBBM allowing infinite initial particles.

Established the coming down from infinity property for these systems.

Characterized the rates at which the process comes down from infinity.

Abstract

The self-catalytic branching Brownian motions (SBBM) are extensions of the classical one-dimensional branching Brownian motions by incorporating pairwise branchings catalyzed by the intersection local times of the particle pairs. These processes naturally arise as the moment duals of certain reaction-diffusion equations perturbed by multiplicative space-time white noise. For the subcritical case of the catalytic branching mechanism, we construct the SBBM allowing an infinite number of initial particles. Additionally, we establish the coming down from infinity (CDI) property for these systems and characterize their CDI rates.