The on/off Brownian snake
Probability
2026-04-03 v1
Abstract
We define what we call an on/off Brownian snake. We use this to construct on/off super Brownian motion recently introduced to the literature by Blath and Jacobi and which is a measure-valued branching process with a dormant state and an active state. Our construction mirrors the construction of super Brownian motion from the Brownian snake by Le Gall. We use the on/off Brownian snake to obtain results concerning the support, range, and expected total mass of on/off super Brownian motion.
Keywords
Cite
@article{arxiv.2604.01852,
title = {The on/off Brownian snake},
author = {Matthew Buckland and Dave Jacobi},
journal= {arXiv preprint arXiv:2604.01852},
year = {2026}
}
Comments
42 pages, 3 figures