Some Explicit Distributions for Brownian Motion Indexed by the Brownian Tree

#### J.-F. Le Gall, A. Riera

2020, v.26, Issue 4, 659-686

ABSTRACT

We derive several explicit distributions of functionals of Brownian motion indexed by the Brownian tree. In particular, we give a
direct proof of a result of Bousquet-M\'elou and Janson identifying the distribution of the density at $0$
of the integrated super-Brownian excursion.

Keywords: Brownian snake, tree-indexed Brownian motion, occupation measure, integrated super-Brownian excursion, local time, exit measure