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.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Département de mathématiquesUniversité Paris-Sud and Institut universitaire de FranceOrsay CédexFrance

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