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October 2001 A Vervaat-like path transformation for the reflected brownian bridge conditioned on its local time at 0
Philippe Chassaing, Svante Janson
Ann. Probab. 29(4): 1755-1779 (October 2001). DOI: 10.1214/aop/1015345771

Abstract

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.

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Philippe Chassaing. Svante Janson. "A Vervaat-like path transformation for the reflected brownian bridge conditioned on its local time at 0." Ann. Probab. 29 (4) 1755 - 1779, October 2001. https://doi.org/10.1214/aop/1015345771

Information

Published: October 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1032.60076
MathSciNet: MR1880241
Digital Object Identifier: 10.1214/aop/1015345771

Subjects:
Primary: 60J65
Secondary: 60C05 , 68P10 , 68R05

Keywords: Brownian bridge , Brownian excursion , hashing with linear probing , Local time , parking functions , path transformation , Profile

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 4 • October 2001
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