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arXiv · 2005.09880

Path decompositions of perturbed reflecting Brownian motions

Elie Aïdékon·Yueyun Hu·Zhan Shi
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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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Elie Aïdékon, Yueyun Hu, Zhan Shi. 2020-05-20. Path decompositions of perturbed reflecting Brownian motions. https://arxiv.org/abs/2005.09880

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