The Annals of Probability
- Ann. Probab.
- Volume 29, Number 4 (2001), 1755-1779.
A Vervaat-like path transformation for the reflected brownian bridge conditioned on its local time at 0
We describe a Vervaat-like path transformation for the reflected Brownian bridge conditioned on its local time at 0: up to random shifts, this process equals the two processes constructed froma Brownian bridge and a Brownian excursion by adding a drift and then taking the excursions over the current minimum. As a consequence, these three processes have the same occupation measure, which is easily found.
The three processes arise as limits, in three different ways, of profiles associated to hashing with linear probing, or, equivalently, to parking functions.
Ann. Probab., Volume 29, Number 4 (2001), 1755-1779.
First available in Project Euclid: 5 March 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Chassaing, Philippe; Janson, Svante. A Vervaat-like path transformation for the reflected brownian bridge conditioned on its local time at 0. Ann. Probab. 29 (2001), no. 4, 1755--1779. doi:10.1214/aop/1015345771. https://projecteuclid.org/euclid.aop/1015345771