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.
Publié le : 2001-10-14
Classification:
Brownian bridge,
Brownian excursion,
local time,
path transformation,
profile,
parking functions,
hashing with linear probing,
60J65,
60C05,
68P10,
68R05
@article{1015345771,
author = {Chassaing, Philippe and Janson, Svante},
title = {A Vervaat-like path transformation for the reflected brownian
bridge conditioned on its local time at 0},
journal = {Ann. Probab.},
volume = {29},
number = {1},
year = {2001},
pages = { 1755-1779},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345771}
}
Chassaing, Philippe; Janson, Svante. A Vervaat-like path transformation for the reflected brownian
bridge conditioned on its local time at 0. Ann. Probab., Tome 29 (2001) no. 1, pp. 1755-1779. http://gdmltest.u-ga.fr/item/1015345771/