TL;DR
This paper introduces the on/off Brownian snake, a new stochastic process, and uses it to construct and analyze on/off super Brownian motion, a measure-valued branching process with dormant and active states.
Contribution
It defines the on/off Brownian snake and applies it to construct and study the properties of on/off super Brownian motion, extending previous models.
Findings
Provides support and range properties of on/off super Brownian motion.
Analyzes the expected total mass of the process.
Constructs the process using a novel on/off Brownian snake framework.
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.
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