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- Publisher
- Springer International Publishing
- Copyright
- © Springer Nature Switzerland AG 2021
- ISBN
- 978-3-030-83308-4
- Pages
- 13 –42
- DOI
- 10.1007/978-3-030-83309-1_2
- Publisher site
- See Chapter on Publisher Site
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 (Probab Theory Relat Fields 4:197–217, 2004) and Le Jan (Ann Probab 38:1280–1319, 2010; Markov Paths, Loops and Fields. École d’été Saint-Flour XXXVIII 2008. Lecture Notes in Mathematics vol 2026. Springer, Berlin, 2011), in particular on a result discovered by Lupu (Mém Soc Math Fr (N.S.) 158, 2018) identifying the law of the excursions of the PRBM above its past minimum with the loop measure of Brownian bridges.]
Published: Jul 30, 2021
Keywords: Perturbed reflecting Brownian motion; Path decomposition; Brownian loop soup; Poisson–Dirichlet distribution