Bessel processes, the Brownian snake and super-Brownian motion

Abstract

We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the Brownian snake conditioned on the minimizing path.

arXiv commentSubmitted to the special volume of Séminaire de Probabilités in memory of Marc Yor