English

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

R2 v1 2026-07-01T11:50:42.912Z