The Annals of Probability

A Vervaat-like path transformation for the reflected brownian bridge conditioned on its local time at 0

Philippe Chassaing and Svante Janson

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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.

Article information

Source
Ann. Probab., Volume 29, Number 4 (2001), 1755-1779.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1015345771

Digital Object Identifier
doi:10.1214/aop/1015345771

Mathematical Reviews number (MathSciNet)
MR1880241

Zentralblatt MATH identifier
1032.60076

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60C05: Combinatorial probability 68P10: Searching and sorting 68R05: Combinatorics

Keywords
Brownian bridge Brownian excursion local time path transformation profile parking functions hashing with linear probing

Citation

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


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