Jean‐François Le Gall, Armand Riera
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-Melou and Janson identifying the distribution of the density at 0 of the integrated super-Brownian excursion.
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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-Melou and Janson identifying the distribution of the density at 0 of the integrated super-Brownian excursion.
Key concepts: Brownian excursion, Brownian motion, Reflected Brownian motion, Excursion, Geometric Brownian motion, Mathematics, Diffusion process, Martingale representation theorem