Bessel processes, the Brownian snake and super-Brownian motion

2014/07/01 by Jean-François Le Gall, Gall, Jean-François Le
Mathematics · #60J68 #60J80 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J68 #msc:60J80

paper · pdf · doi:10.48550/arxiv.1407.0237

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

arxiv created 2014/07/01 · arxiv updated 2014/07/02

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.

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