Path decompositions of perturbed reflecting Brownian motions

2020/05/20 by Aïdékon, Elie, Hu, Yueyun, Shi, Zhan
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2005.09880

Abstract

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.

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