Path decompositions of perturbed reflected Brownian motions

Elie Aïdékon (1) , Yueyun Hu (2) , Zhan Shi (3)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

We are interested in path decompositions of a perturbed reflecting Brownian motion (PRBM) at the hitting times and at the minimum. Our study relies on the loop soups developed by Lawler and Werner [10] and Le Jan [13]-[14], in particular on a result discovered by Lupu [15] identifying the law of the excursions of the PRBM above its past minimum with the loop measure of Brownian bridges.

Mots clés: Perturbed reflecting Brownian motion; Path decomposition; Brownian loop soup; Poisson-Dirichlet distribution

Domaines: Probabilités [math.PR]

Elie Aïdékon, Yueyun Hu, Zhan Shi. Path decompositions of perturbed reflected Brownian motions. 2020. ⟨hal-02612935v1⟩